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High resolution electron scattering facility at the Darmstadt linear accelerator (DALINAC)
NUCLEAR
INSTRUMENTS
AND METHODS
153 ( 1 9 7 8 )
17-28;
©
NORTH-HOLLAND
PUBLISHING
CO.
H I G H R E S O L U T I O N E L E C T R O N S C A T T E R I N G FACILITY AT T H E D A R M S T A D T LINEAR A C C E L E R A T O R (DALINAC) * II. BEAM T R A N S P O R T S Y S T E M AND S P E C T R O M E T E R (ENERGY-LOSS SYSTEM) TH. WALCHER*, R. FREY, H.-D. GRAF, E. SPAMER and H. THEISSEN**
Institut .fur Kernphysik, Technische Hochschule Darmstadt, 61 Darmstadt, West Germany
Received 22 November 1977 Design and installation of a high resolution energy-loss electron scattering system at the Darmstadt linear accelerator are described. The apparatus consists of a beam transport system with two 70°-dipole bending magnets, eleven quadrupole focussing
magnets, a five quadrupole magnet set as rotating element, and a magic angle (169.7°) spectrometerfor analyzing the scattered electrons. For a primary momentum spread Ap/po = 3 x 10-3 , a spectrometer acceptance solid angle 0 = 5 msr, and a 10 mg/cm 2 thick Be target, the Tesolution was measured to be 6p/p o = 4x 10 - 4 , equivalent to 25 keV for 60 MeV electrons.
1. Introduction This article is the second of a series of four papers about the new high resolution electron scattering system at Darmstadt. Article 11) dealt with improvements of accelerator (injector and RF driver) and v a c u u m system. In this paper design and installation of beam transport system and spectrometer are described. A conventional electron scattering apparatus with an achromatic beam transport and analyzing system has the disadvantage that a sizable portion of the beam current is lost in the analyzing system where the m o m e n t u m spread of the primary beam is cut down to a value compatible with the desired overall resolution. The D A L I N A C m o m e n t u m spread, for instance, is of the order of A p / p o - ~ 3 x l O -3 (fwhm, see I), about ten times larger than the desired resolution @ / p ~ 3 x 10 4, so that only one tenth of the accelerator beam current could be used in a high resolution experiment. Since high resolution experiments, in any case, suffer from low counting rates due to target thickness limitations imposed by energy straggling, severe reductions in beam current are not tolerable. The possibilities to improve on the D A L I N A C m o m e n t u m spread are limited (see I). For this reason, the " e n e r g y - l o s s " - or "dispersion matching" - m e t h o d (e.g. see ref. 2, 3) was employed. t
Supported by the Bundesministerium for wissenschaflliche Forschung and the Deutsche Forschungsgemeinschaft. * Now at: Max-Planck-Institut ftir Kernphysik, Heidelberg. ** Now at: Gymnasium Mt~nchen-Gladbach-Odenkirchen, Mt~nchen-Gladbach.
Its basic principle is to match the dispersion of the beam transport system to that of the spectrometer such that the entire apparatus (starting at the accelerator exit) is non-dispersive in the spectrometer focal plane. This makes the system sensitive only to the energy loss in the target and not to the m o m e n t u m spread of the beam hitting the target. As a consequence, m o m e n t u m analyzing slits in the beam transport system are not required, so that beam currents comparable to those obtained with conventional systems of moderate resolution are usable. Target thicknesses, however, are limited, due to energy straggling, as in the conventional case. More stringent than in the conventional mode of operation are the requirements for accelerator stability and target uniformity. The reason is the dispersion of the beam on the target, stretching the beam spot out into a strip. The notation used in this article is consistent with that of Brown 4'5) and the one used in code T R A N S P O R T 6) which has been employed in most of the ion-optical calculations.
2. Beam transport system Fig. 1 of I shows the ground plan of the Darmstadt accelerator building. Analyzing system AS1, quadrupoles Q~, Q2 and the 120° spectrometer (120°-Sp.) are elements of the old electron scattering systemT). The switch to the new system is the 70°-dipole magnet M1 downstream of Q~ and Q2. Together with the other 70°-dipole magnet M2 and the six quadrupoles D1, S1 and $2, D2 it forms a second m o m e n t u m analyzing system with slits ES2 in the s y m m e t r y plane between M1 and M2. The rotator R, a set of five quadrupoles, is
18
TH. W A L C H E R et al.
used to turn the dispersion plane in the energy loss mode of operation, and the quadrupole triplett T focusses the beam onto the target. A quadrupole doublet behind the target reduces the beam divergence due to multiple scattering and delivers it to a Faraday cup which simultaneously serves as current monitor. The scattered electrons are momentum analyzed in a high resolution "magic angle" spectrometer (169°-Sp.). Design and arrangement of the new high resolution system were determined by the free space in the building and the condition that the old low resolution system should be further operable. Although designed as an energy-loss system, the new scattering apparatus may also be operated conventionally. In this case, the quadrupoles D1, M1 I
I
D1
$1
IlU
U
S2 D2 U ULI
S1 and $2, D2 are powered symmetrically such that the system is achromatic. Fig. 1 shows the characteristic trajectories for this mode of operation. They were computed on the DESY analogue computer8,9). Assuming an incident beam parallel to the optical axis (emittance e = 0), trajectory Cx = (xlx), is representative. This trajectory intersects, as fig. 1 shows, the optical axis at three points, viz. between M1 and D1, between S1 and $2, and between D2 and M2. All three points are focal points with non-zero dispersion Dx--(xl6). The momentum defining slits ES2 are installed at the focal point between S1 and $2, which coincides with the symmetry plane of the system. At this position, D~ has its maximum value 4.89 cm/% and, as required for an achromatic sys-
M2 I
T1 UUU
I
1.0t x/cm Dx
15 7
~
.
20
Cx -05-
-1.0-
Y/cm
1.0
Cy
0.55 I
\
20 ',
Sy -Q5- 1.0-
Fig. 1. Characteristic trajectories in the convetional mode of operation. - 0 . 1 % . D x ; 1.1 c m . C y ; and 0.75 mrad.Sy.
The
curves
represent
0.25cm.Cx;
2 mrad-S x ;
19
HIGH RESOLUTION ELECTRON S C A T T E R I N G F A C I L I T Y II TABLE 1
Matrix elements of 0" measured upstream of quadrupole doublet Ql Q2 for 90% of total beam current. Accuracy about ___20%. PG: Pierce gun, Hl: Haimson Injector.
Injector
E
v' (711
v' 0 22
0.21
8x
v o33
v' 0-44
0.43
8y
(MeV)
(cm)
(mrad)
(cm mrad)
(cm mrad)
(cm)
(mrad)
(cm mrad)
(cm mrad)
60 50 50 40
0.20 0.25 0.18 0.37
0.20 0.20 0.32 0.30
0.007 0.022 0.041 0.020
0.039 0.047 0.038 0.110
0.38 0.42 0.26 0.44
0.68 0.70 0.23 0.69
0.26 0.29 0.06 0.29
0.023 0.041 0.017 0.100
PG PG H1 PG
tern, is parallel to the optical axis. Additional slits at the two other focal points serve to reduce the beam halo. In order to study the imaging properties of the system for non-zero emittance (s:~0), the emittance of the DALINAC beam was determined 1°) by measuring beam profiles before and after quadrupole doublet Q1 Q2. From these data and the known transformation matrix of the doublet, matrix elements of the beam matrix a were calculated. The beam profiles were determined by counting fission product tracks in mica resulting from electrofission on Bi. The beam diameter was defined as the width of the distribution at 1/5 of the maximum (equivalent to about 90% of the total current). Table 1 contains the matrix elements of crx and try obtained in this way for a position just upstream of quadrupole doublet Q1 Q2. Data were taken for three representative energies and two l
types of injectors, the old Pierce-typ one (now out of use) and the new grid-controlled gun (see I). The measured beam emittances were used to calculate, by means of code TRANSPORT6), the trajectory envelopes displayed in fig. 2. It is seen that the incoming beam diverges in y-direction (V/O'44=~-0, see table 1) which is due to the fringe fields of AS1. The doublet Q1 Q2 serves to make it "parallel", i.e. it generates a "bellow" (a21 = a43 = 0). From fig. 2 the resolution of the analyzing system can be estimated as 6p/p = 2 × 1 0 4 (width at 1/5 of maximum). The extension in y-direction of the beam spot on the target is roughly 0.6 mm. This value is sufficiently small for the spectrometer described below. In the energy-loss mode of operation, the beam dispersion on the target has to be matched to that of the spectrometer. Multiplying the transformation matrices of beam transport system (index
x/cm
03-
,/ . . . . .
0.2'
,~
/
0.1'
_jr
v
V
~
¢
v
-...~__
z/m 0.1 ¸ O2 Q3
OA
UUA Q1Q2
i M1
'UU SL1 D1
U $1
SL2
$2
D2 SL3
M2
T
y/cm Fig. 2. Envelopes in the conventional mode of operation calculated for the measured emittance (table 1 : PG, 60 MeV) and dispersion trajectory D x .
20
TH.
WALCHER
BTS) and spectrometer (index SP), and requiring the total dispersion to be zero leads to: (xl6)Brs = - (x[6)sP E° (x[X)sp E o - E x '
(1)
where Eo is the incident electron energy and Ex the nuclear excitation energy (energy loss). The equation is valid for relativistic electrons with E =pc. The margin within which this condition must be fulfilled without appreciable loss in resolution is, for (xlx) p = - 1 , given by:
6p
>
p
ap [1 p-~
Eo-Ex (xl, ).Ts7 Eo
(xl6)sp_]'
(2)
where Ap/po is the primary momentum spread and 6p/p the desired resolution. Apart from meeting condition eq. (1) an energyloss system requires a sufficiently large resolution of the beam transport system at the target. This means that the target beam spot diameter of a monoenergetic component has to be comparable to the one obtained conventionally. Generalizing the considerations for first order momentum resolution of Brown 4'6) smallest resolution R of a beam transport system for an arbitrary beam matrix a is derived as: R = 3p/p = 2e/[~11(0) I 2 + 2cr21(0) 1112 + + a22(0) 12] +1/2 ,
(3)
with:
11 =
f:
Cx(z ) h(z) dr ;
12 =
fo
Sx(z) h(z) az.
In these equations, Cx and Sx are the trajectories (xlx) and (xlO), respectively, h ( r ) = l/p0 is the curvature of the central trajectory, and 0 denotes the entrance and L the exit of the beam transport system. For the beam transport system considered here, 0 stands for the position of the accelerator exit and L for the target position. For a given beam matrix a with emittance e, the integrals I~ and /2 have to be as large as to make R smaller than the desired overall resolution (i.e. R has to be of the order of the spectrometer resolution). For an achromatic system 11 and 12 vanish. Dispersion and resolution of the beam transport system are obtained by powering quadrupoles S1 and $2 asymmetrically. The dispersion generated in this way is horizontal, whereas the spectrometer, due to its upright installation, is dispersive in vertical direction. A vertical installation of the spectrometer is imperative since one needs:
et al.
1) a large range of scattering angles (40°-165°), 2) a good definition of the scattering angle, i.e. a small acceptance angle in the scattering plane, and 3) a large distance between target and detector system (to create space for shielding). For these reasons, the dispersion plane of the incident beam has to be turned through 90° around the optical axis. The device ll) doing this is the rotator (fig. 1 of I), a set of five quadrupoles whose symmetry planes are tilted through 45 ° against normal orientation. Through the rotated symmetry planes, the ordinarily decoupled x- and y-phase spaces are coupled such that, for proper setting of the gradients, the device acts as a fieldfree drift space interchanging x- and y-coordinates. The quadrupole triplet T not only images the beam onto the target but also serves to adjust the dispersion according to eq. (1). This is done by variing the gradients of the two outer quadrupoles of T. The dispersion is adjustable over the range 4 cm/% < (x] 6)BTs< 6 c m / % . For the spectrometer described below and E0 = 60 MeV, this is equivalent to excitation energies between 0 and 20 MeV. Since the resolution is constant down-stream of M2 (h(r)=0) for a fixed optical mode [eq. (3)], variation Of the dispersion changes the beam spot size and hence the line profile in the spectrum. This is of particular importance for low energy accelerators where the ratio Ex/Eo is large. Fig. 3 shows the beam envelopes for the energyloss mode of operation calculated for the measured emittances (table 1: PG, 60 MeV). The beam spot size on the target is seen to be 0 . 8 × 2 . 0 m m 2 yielding a resolution 6p/p=5×lO 4 (width at 1/5 of maximum). For the dispersion on the target 4 c m / % is obtained a value close to that of the spectrometer. The maximum dispersion behind M2 is 10cm/%. For an inner diameter of the beam pipe of 4 cm this yields a maximum possible momentum spread Ap/p = 0.4%. To avoid excessive background some distance between pipe and beam is desired, so that Ap/p is actually limited to 0.2%.
3. Magic-angle spectrometer The type of spectrometer for the new system was selected according to the following criterions: 1) The resolution should be 3× 10 4 for an acceptance solid angle .(2 = 5 msr and a target beam spot size in vertical direction
21
HIGH RESOLUTION ELECTRON S C A T T E R I N G F A C I L I T Y II
0.4!
x Icm ~\
,~D x- 4 . 1 0
Q3"
-4
/
....
0.2'
,"\
I
,~
~
I I ~'~'~
I I I
I \
I
/'~
//--,,_______~\
0.1
/\
5
/~
lo
I~
~ 15
2o
z/m
o
0.2 0.3
/
'
\1
I ale2
M1
SL1 D1
$1
SL2
$2
D2 SL3
M2
~.
/"
I ROTATOR
T
y/cm
Fig. 3. Envelopes in the energy-loss mode of operation calculated for the measured emittance (table 1: PG, 60 MeV) and dispersion trajectory D x .
2 x0 = 0.1 cm. A m o m e n t u m interval of 3% should be accepted. 2) The linear dispersion should be large enough to permit installation of a scintillator detector system. A set of 36 overlapping plastic scintillators (width 6 m m , length 11 m m and thickness 1.5 mm) yielding 69 channels with a spatial resolution of 0.2 cm (see III) was planned. 3) Inexpensiveness was mandatory. Design, construction and installation should not delay other activities of the laboratory. These requirements are met to a high degree by the so-called magic-angle spectrometer. It is a double focussing sector-field spectrometer with a deflection angle z = ~r v'8/3 = 169.7 °. Devised by Ikegami12), it was propagated by Penner and Lightbodye3), who demonstrated its advantage for electron scattering experiments. It is now used in many electron scattering facilities14-16). Instruments with better ion-optical properties, as for instance a splitpole spectrometer2), were not considered because of their high cost. The magnetic field in the spectrometer midplane is described by the usual expansion: By = B o [1 - n(x/ro) + fl(x/ro) 2 - y(x/ro) 3 + ...], (4)
x being the radial distance from the center trajectory and r0 the radius of the center trajectory. Since n = 0.5 is necessary to obtain double focussing, o n l y / / and 7 are optional. To facilitate manufacturing conical pole shoe faces yielding B = 0.25 and 7 = 0 . 1 2 5 were chosen. The deflection angle r = 169.7 °, together with the straight yoke edges at entrance and exit, makes the second order error (xlO2) vanish for all object distances. Error (xl06) is, as usual, eliminated by tilting the focal plane with respect to the center trajectory through the angle or given by: tan cc = - (010) (xl~)/(xlO~), (5) in this case o~-~35 °. Due to this angle, the detector channel width is halvened to 1 ram. Elimination of the aforementioned second order errors ensures satisfactory performance in the conventional mode of operation. It also suffices for the energy loss mode of operation if precautions are taken to reduce the effect of matrix elements (xlx 2) and (xlxO). These errors are important since the target beam spot size (object size) Xo=(X[6)B~sAp/Po is no longer small. The spectrometer described here has an acceptance angle in radial direction 00-~ ___60 mrad, so that even for a m o m e n t u m spread as small as Ap/po= ___0.15% error (xlxO) limits the resolution.
22
TH. WALCHER et al.
TABLE 2 4. Design, construction and test of quadrupoles, Parameters of beam transport system magnets. bending magnets and soectrometer All magnets including power supplies were Quadrupole magnets: 12.00 cm manufactured, according to plans of the Institut Geometric length 12.64 cm for Kernphysik, by Lintott Engineering Ltd., Hor- Effective length 2.75 cm sham, Sussex, England. In the design of the mag- Aperture radius Maximum gradient 1.3 kG/cm nets, special attention was paid to field uniformity Maximum current 20 A of the dipole magnets, small amplitudes of higher Maximum power 240 W air harmonics in the quadrupoles, and, in general, Cooling 118 kg short fringe fields. The quadrupoles (D1, S1, $2, Weight D2, T) are slightly modified reduced size copies of Dipole magnets: the DESY standard construction9,17). Their paRadius of center trajectory 1.00 m rameters are summarized in table 2. Tolerances in Gap width 5.00 cm machining the pole shoe contours were set to Vacuum chamber (inside cross-section) 4.3 × 8.0 cm 18-120 MeV _+0.02 ram. Hyperbolically shaped edges and mir- Energy range 0.6--4.0 kG ror plates at entrance and exit ensured a short and Field strength Maximum current 250 A almost linear fringe field, the shape being inde- Maximum power 6 kW pendent of field strength. For all quadrupoles the Cooling water 1.3 t gradient was measured as a function of distance Weight 70.0° _+0.1 ° along the optical axis. A temperature-stabilized Deflection angle Field uniformity _+ 10 -4 and compensated Hall plate (Siemens SBV 579) Slope of entrance edge MI 25.0°_+0.5 ° with a relative accuracy of _+2×10 -4 (_+0.4G Slope of exit edge M2 minimum) was used as field probe. It was mount- Slope of exit edge M1 0.00_+0.5 ° M2 ed on a lathe tool carriage permitting semi-auto- Slope of entrance edge matic movements in three directions. The measurements yielded an effective length of 126.4 mm for all quadrupoles, the deviation from this aver- mated with the help of TRANSPORT 6) were age value being less than _+0.2 mm. The propor_+0.1 mm. An accurate determination of the magtionality between gradient and exciting current netic axis of each quadrupole was therefore manwas measured to be better than _+10-3 , a value datory. It was carried out after the method of Cobb achieved by giving the quadrupoles a large pole and Murray 23) and yielded accuracies of better basis. The results of the field measurements were than _+0.03 mm~8). The axis coordinates were dealso used as input data for ray-tracing calculations termined relative to two adjustment cross-wires on with the code RAY-TRACINGS9'2°). These calcu- top of the quadrupole yoke. The bending magnets lations and additional floating wire experiments 21) were furnished with identical cross-wires mounted showed that the theoretical first order focal in the same height above the beam line. This falengths were reproduced, for the gradients used cilitated an accurate installation of the entire syshere, to within _+0.3%. As a further test, the tem. quadrupole field was subjected to a harmonic analThe bending magnets M1 and M2 are H-type ysis according to the method of Haibachn). The dipole magnets with one of the two edges (enrelative amplitudes of higher harmonics (multipole trance edge of M1 and exit of M2) sloped by 25 ° field strength divided by quadrupole field strength, for vertical focussing. The pole shoes on both both measured at the aperture radius of 2.75 cm) edges have a threefold bevel approximately formmeasured in this way were less than 2× 10 -4 ex- ing a hyperbola. Together with the mirror plates, cept for a 3% contribution of the duodecapole am- this ensures a short and linearly decreasing fringe plitude (allowed multipole component of lowest field independent of excitation. Displacement and order). slope of the beam (with respect to the center traThe adjustment tolerances of the system esti- jectory) after traversing the magnet are thus expected to be negligible24). Measurements of the fringe field with the aforementioned Hall probe The measurements were kindly performed by Dr. Langenbeck, GSI, Darmstadt. and subsequent ray-tracing calculations confirmed
HIGH
RESOLUTION
ELECTRON
this2~). The effective field boundary coincided with the geometrical edge to within better than 0.4 m m , so that the effective deflection angle was 70.0°+_0.1 °. Filter gaps 2s) secured a high uniformity of the main field (see below). Measurements with an N M R probe 21) yield a m a x i m u m variation in field strength of ___10 -4 over a range of _+4 cm perpendicular to the beam axis for fields between 0.6 and 4 kG. The pole shoe width, for comparison, is 20 cm. Further parameters and properties of the magnets are listed in table 2. The limitations in resolution due to finite detector system channel width (1 mm) and beam spot diameter on the target ( ~ 1 mm) require a spectrometer with a large radius. A large radius, on the other hand, makes it difficult to shape the field precisely according to eq. (4) since the field strength is small. The reasons are the small permeability and the remanent magnetism at field strengths below 1 kG for normal high grade magnet iron (carbon content <0.07%). As a tolerable compromise, a radius of 1 m was chosen, so that, for fields between 0.6 and 4 kG, electrons with 18 MeV to 120 MeV energy are analyzed. Table 3 lists the main construction parameters of the spectrometer. Since the m a x i m u m field strength used in the experiments is small (2.3 kG for 70 MeV electrons), it was sufficient to close the magnetic flux through the inner part of the sector. The resuiting C-shape yoke has the advantage that the TABLE 3 Parameters of spectrometer. Radius of center trajectory Gap width Vacuum chamber inside cross-section open back Energy range Field strength Maximum current Maximum power Weight spectrometer shielding (safe load) Deflection angle Field coefficients n fl y Object distance Image distance Entrance and exit angle Curvature of pole edges
1.00 m 10.0 cm 7.5 c m × 26 cm 30 ° < cz< 150° 18-120 MeV 0.6-4.0 kG 280 A 25 kW 17 t 10 t 169.6°-+0.1 ° (169.7°-+0.1 °) 0.5036_+0.0023 (0.500) 0.259 _+0.008 (0.250) 0.09_+0.07 (0.125) 0.87 m 0.65 m (0.78 m) 0.0_+0.1 ° (0°) 0 (0)
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FACILITY
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23
spectrometer is iron free on the back. N e u h a u s e n and Fricke 26) have demonstrated that this reduces background in inelastic scattering if, in addition to that, the v a c u u m chamber on this side is sealed with a thin foil. The reason is that backscattering from the chamber walls or other material is reduced. Because of the unusual design of the spectrometer (C-type yoke and low field strengths) the field distribution in iron and gap was calculated with code TRIM27,28). This programm solves, by means of a finite difference method, the vector potential problem for a given relation between permeability and field strength. Fig. 4 shows the cross-section of the magnet with the calculated field lines for a spectrometer with and without filter gap. The effect of the filter gap is clearly visible. The field lines leave the iron less oblique (with respect to the pole shoe planes) than in the case without filter gap. Another advantage is that the field configuration depends only weakly on exciting current. The shims at the pole shoe edges seen in fig. 4 extend the range in radial x-direction over which the field follows eq. (4). The field was measured 29) with a rotating coil instrument ( R a w s o n - L u s h model no. 924/944) of a relative accuracy of +_2×10 -5 and the aforementioned Hall probe which had the same relative accuracy for differential measurements. Data were taken for three deflection angles (65 ° , 87 ° and 119°). Systematic deviations among the results for the three angles were not observed and a dependence of the field pattern on exciting current could not be detected. The mean values of the field coefficient for - 10 c m < x < 10 cm from all measurements were: n = 0.5036_+0.0023, fl = 0.258 _+0.008, ? = 0.09 +0.07. A least squares fit of By according to eq. (4) to the field calculated with TRIM27,28), on the other hand, yielded for the same interval: n = 0.4975, 13 = 0.232, ? = 0.08. The deviation between measurement and calculation could not be fully explained. Insufficient accuracy of the computer code was ruled out since the results were to a high degree independent of the pivotal points. Qualitative agreement with the
24
TH. W A L C H E R et al.
iiiiil IIIIIlll
/ I
i
Fig. 4. Field lines in magic angle spectrometer with and without filter gap.
result of conformal mapping corroborated this. A probable explanation is a local permanent magnetization of the pole shoes at x = - 1 7 cm and + 19 cm caused by magnetic welding seams of the first (stainless steel) vacuum chamber. This chamber was later replaced by a non-magnetic one. The deviations between actual and ideal field coefficients have only minute effects on the spectrometer optics. As the bending magnets, the spectrometer has a threefold, approximately hyperbolic, bevel at the yoke edges and mirror plates in order to linearize the fringe field. The effective field boundary which defines the actual deflection angle deviates by (0.15_+0.05)cm from the geometrical edge of the iron. This yields a deflection angle r = 169.6°_+0.1 °. The field parameters measured for the spectrometer were used to calculate its imaging properties. This was done with code RAY TRAC-
ING 19,2°) modified such that the variation of n in the fringe field was taken into account. The code evaluates, by integrating 44 trajectories, matrix elements of up to fourth order. The result is listed in table 4, column A. For comparison, calculations with RAY TRACING for a constant n in the fringe field and TRANSPORT have been performed, the results being displayed in columns B and C, respectively. In order to reach scattering angles up to 165 ° the object distance (distance between target beam spot and spectrometer effective field boundary) was chosen to be do = 87.0cm. For this do, the first order image distance (distance between spectrometer effective field boundary and intersection of center trajectory with radial focal plane) is calculated to be dlX)= 78.4 cm, whereas RAY TRACING 19'2°) yielded 71.1 cm. The measured image distance (see III) was dlX~= 66.5 cm. An explanation of the discrepancy cannot be given.
HIGH
RESOLUTION ELECTRON
TABLE 4 Transformation matrix elements of magic-angle spectrometer for the focal plane calculated with RAY TRACING19,2°). Units are cm, mrad and %. Power of ten in parentheses. A: measured field with n = 0.5036, /3= 0.2598, y =0.0932, linear fringe field with measured n=n(z), object distance d o = 87.0 cm, image distance d I = 70.8 cm and angle between focal plane and center trajectory ~ = 34.9 °. B: design with n = 0.5,/3 = 0.25, 7 = 0.125, linear fringe field with n = 0.5 over entire range, d o = 87.0 cm, d I = 76.0 cm and ~ = 33.9 °. C : result of calculation with TRANSPORT 6) for comparison, n = 0 . 5 0 3 6 , /3=0.2598, ~=0.0932, linear fringe field with K I = 0.33 ; K2 = 0.0, d o = 87.0 cm, d I = 78.4 cm and ~z= 33.9 °. Matrix element
(xlx) (xl 0) (xl 5) (YlY) (vl 0)
(OIx) (010) (0[6) (OlY) (0[0) (xlx 2)
(xlxO) (x[x6) (x[O 2)
A
-
-
-
(x106) (xly 2)
(xlyO) (xlO 2) (x162) (xlO 3) (xlO02)
(xlxO2) (xlx 2 O)
(x1026) (xt 062) (xlxO 2) (x] 02 6) (x]O4) (x] 02 02) (x10262) (xl 04)
-
-
0.955 0:000 3.760 0.885 0.017 5.606 1.046 10.768 6.785 0.993 7.580(-3) 1.419(-3) 2.961(-2) 1.190(-6) 4.631 ( - 6 ) 1.126(-2) 9.503(-4) 1.480(-4) 6.217(-2) 1.294(-7) 7.183(-7) 1.172(-6) 7.808(-6) 4.778(-6) 1.516 ( - 4 ) 2.115(-6) 1.841 ( - 6 ) 7.165(-11) 1.969 ( - 10) 3.551(-8) 2.878 ( - 10)
Value B
C
0.966 - 0.974 0.000 0.000 3.921 3.977 0.945 - 0.971 0.006 0.000 6.136 - 6.126 1.034 - 1.027 12.225 12.344 6.444 - 6.438 1.013 - 1.027 8.486(-3) 8.430(-3) 1.434(-3) 1.411 ( - 3 ) 3.335(-2) - 3.361(-2) 0.000 - 2.656(-6) 2.536 ( - 4 ) 2.403 ( - 4 ) 1.211(-2) - 1.185(-2) 9.492(-4) - 9.101(-4) 1.470(-4) - 1.347(-4) 7.210(-2) 7.283(-2) 8.706(-8) 5.315(-7) 8.562(-7) 6.474(-6) 3.394(-6) 1.991 ( - 4 ) 1.862(-6) 3.938 ( - 7 ) 8.631(-11) 3.865 ( - 10) 7.433(-8) 2.480 ( - 10)
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FACILITY
11
25
The angle cz between focal plane and center trajectory depends mainly on /3 and is insensitive to variations of the fringe field gradient. From table 4 one obtains ~ = 350___0.5°. The transformation matrix elements (table 4) supplied by RAY TRACING 19,2°) were finally used to calculate the intrinsic resolution of the spectrometer. Initial coordinates of about 105 particles uniformly distributed over the phase space given by beam spot size, spectrometer acceptance solid angle, etc. were therefore transformed into the focal plane. For the conventional mode of operation, the phase space contour was taken to be x 0 = 0 , Y0=+-0.1cm, 00= + 6 0 m r a d , and 00 = ___18 mrad, equivalent to a monochromatic line source and an acceptance solid angle of 4.3 msr. For the energyqoss mode of operation, a source with x0= +_0.5cm, corresponding to Ap/po= +_0.13% (the monoenergetic spot size is zero), and otherwise same parameters was assumed. All matrix elements up to fourth order were taken into account. The result is shown in fig. 5. It is seen that the line widths (fwhm), for a momentum range of _1.5%, are smaller than 1 . 5 X 1 0 - 4 . Since the contributions of detector width and beam spot size a r e 3 x l 0 -4 and ,
10
,
r
,
i
,
,
f
,
6 = 0,0%
~
ZI;K <11<3
'
=/,
,
conventional
-1.5%
i
* 1.5°1°
1.2'10 -4
' . . . . . . . energy 8=0.0,1,
1 4 10 4
,
mode
1.2"10 4
'
, ' ' loss mode
1.4.10 4
.4.10.4
5
Radial image distance dl ~) and axial image distance dl y) are interrelated. For the difference dlY)-dl x)= --(Ylq~)/(q~lq~) one obtains 17 cm. For an acceptance angle 00 = ___20 mrad this astigmatism causes an axial image width of 9 mm in the focal plane. Since the scintillation counter of the detector system are 11 mm wide in y-direction, the angle 00 had to be reduced to ± 15 mrad to avoid fluctuations in counting rate due to drifts of the target beam spot position (see III).
_55-s5"'-o.~o'.o61
'~'' 5.7
5:9
x/cm
Fig. 5. Upper part: intrinsic line profile for the conventional mode of operation in the focal plane caused by spectrometer aberration errors up to fourth order. Line source with phase space boundaries x 0 = 0 , Yo = _+0.1 cm, 00 = _+60 mrad, and 0o = _+18 mrad; x is the distance to the center trajectory; 5 denotes the relative m o m e n t u m difference. Lower part: same for the energy-loss mode of operation, x 0 = 0.5 cm, equivalent to Ap/p o =_+0.13% (see text), Y0, eo and 00 as before.
26
TH. W A L C H E R et al.
TABLE 5 Imaging properties of magic angle spectrometer. Maximum radial acceptance angle 00max Maximum axial acceptance angle O0max Maximum solid acceptance angle 3"2max Dispersion Momentum interval accepted Resolution (point source, fwhm) Tilt of focal plane
_+75 mrad ± 2 0 mrad 6 msr 3.76 c m / % _+ 1.5% 0.015% 35 °
2 x 10 4, respectively, this is tolerable. The imaging properties of the spectrometer are summarized in table 5. The spectrometer rests on a 360 ° turntable whose height is adjusted by 84 screws. The maxi m u m deviation of the rotation axis from its mean position was measured to be 0.2 m m , the angle between spectrometer s y m m e t r y plane and axis of rotation to less than _+0.3 mrad. The scattering chamber is a modified version of the construction described by G u d d e n e t al.7). Borings at 12 ° intervals and auxiliary flanges permit the spectrometer to be set to 13 scattering angles between 57 ° and 165 ° . The power supplies are current stabilized with a (short and long time) stability of ± 2 x 10 5 for the dipole and _+10 4 for the quadrupole magnets. Each unit has a digital-to-analogue converter (DAC) with a resolution of 10 5 and a stability of _+2 × 10 6 as reference source. The reference voltage is remotely controlled in the analogue branch. All D A C ' s are linked to a digital master set which allows simultaneous stepping up or down of relative settings. The system may thus be quickly adjusted to changes in electron energy leaving only small corrections to be done by hand. The spectrometer power supply obtains its reference signal from a rotating coil which measures the field strength. The control unit of the rotating coil was modified 3°) such that it automatically locks on the digitally given field strength.
5. lon-optical test T h e beam is threaded through the magnet system with the help of two pairs of Helmholtz coils, one upstream of Q1 Q2, the other between M2 and the R O T A T O R . To determine the beam intensity profile at the target position, a tantalum wire (diameter 0.1 ram) was swept up and down through the beam and the secondary electron current measured as a function o f wire position. Fig. 6 shows
Fig. 6. Beam intensity on the target as a function of distance in vertical direction. Upper part: conventional mode of operation. Middle part: five beam spots in the energy-loss mode of operation, slit width of analyzing system (ES2, fig. 1 of I) 3p/p o - 2 x 10 -4. Slit positions 3p/p o - ± 0 . 1 % , _+0.05% and 0% (see text). Lower part: dispersive beam spot for a primary width of 3P/Po~ _+0.1%. Scale factor 1.25 cm/div.
HIGH R E S O L U T I O N
ELECTRON
the result. In the conventional mode of operation the beam spot is seen to be 0.8 mm wide (upper part of fig. 6). The intensity distributions of the monoenergetic component in the energy loss mode of operation (middle part of fig. 6) were obtained with the momentum defining slits ES2 (fig. 1 ofI)being open to Ap/po = 2 x 10 -4 and setting them together in parallel to Ap/po = 0 , -+-5.10 4 and ±10 3. For a dispersion of 4 c m / % on the target, the lines are expected at x = 0, ±2 and ± 4 mm. From fig. 6 one obtains x = - 3 . 9 , - 2 . 0 , 0.1, 2.1 and 4 . 2 m m with art error of about ±0.1 mm. The dispersion (xl6)sp = (4.1 ±0.1) cm/% following from these values is, according to eq. (2), sufficiently accurate. The line width (~ 1.3 mm) is about 40% smaller than calculated with the measured emittances. If the broadening (x/6)aTsAp/Po= 0.8 mm due to dispersion is taken into account, the line width of the monoenergetic component in the energy loss mode of operation is comparable to that of the conventional mode. The lower part of fig. 6 shows the dispersed beam spot obtained with the slits ES2 opened to ±10 -3. To test the over-all resolution of spectrometer and beam transport system3~), a single plastic scintillator with a width of 1 mm was mounted in the spectrometer focal plane and the line widths of electrons scattered elastically from a 11 mg/cm 2 thick Be target were measured. The result is shown in fig. 7 where the halfwidths (fwhm) 6p/p of the elastic peak have been plotted as a function of slit width Ap/p o of the analyzing system. The acceptance solid angle of the spectrometer was ,Q = 4.8 msr (20o = 120 mrad, 2~0 = 40 mrad) in this measurement. In the conventional mode of 30
i
i
SCATTERING
FACILITY
ii
27
operation the resolution, as expected, increases, from a initial value of 3.7x 10 4, proportional to Ap/po. Since the intensity of the primary beam transmitted through the slits is not constant (fig. 6, lower part), 6p/po is even smaller than 3p/po. In the energy loss mode of operation the resolution is constant and has the value 4.2× 10 -4. In the conventional mode of operation, the peak half width comprises the contribution of beam spot size (1.2 × 10-4), spectrometer intrinsic resolution (1.2× 10-4), detector width (3x 10 4) and energy spread Ap/po of the primary beam. For Ap/po = 1.5 × 10 -4, for example, the quadratic sum of all contributions is 6p/po = 3.8× 10 4, in agreement with the value obtained from fig. 7. In the energy loss mode of operation the beam spot size contributes !.9× 10 4, the spectrometer 1.4× 10 4 and the detector width, as before, 3× 10 4. Since the energy spread of the primary beam does not enter, one obtains 6p/po = 3.8× 10 -4. The discrepancy between this value and the measured one is probably due to an under estimate of the different contributions (see III). 6. Conclusion The apparatus described in this article is the first electron scattering energy-loss system set into operation. Its overall resolution was measured to be 4× 10 4 for a thin target. Since a primary momentum spread of up. to 0.3% is permissible, a great fraction of the accelerator current (--~25 ~A) may be used.
It has been demonstrated that the energy-loss principle may be successfully employed to increase the resolution of electron scattering experiments without appreciable reduction in beam intensity.
i
; ?; oot,ooo, modo References ,~ 20 0 )< o tn [D_ ~o
10
I
0
10
2'0
3'0
Ap/PoXl04 Fig. 7. Resolution 6p/p measured with a single counter as function of primary width Ap/p o.
l) H.-D. Gr~if, H. Miska, E. Spamer, O. Titze and Th. Walcher, Nucl. Instr. and Meth. preceding article. 2) S. B. Kowalski, W. Bertozzi and C. F. Sargent, in Medium energy nuclear physics with electron linear accelerators, MIT 1967 Summer Study, ed. W. Bertozzi and S. Kowalski, USAEC report no. TID-24667 (1967). 3) S. B. Kowalski, in Proc of the Int. Conf. on Photonuclear reactions and applications, Asilomar (1973) Calif., USA, ed. B. L. Berman, USAEC report no. CONT-730301. 4) K. L. Brown, SLAC-report no. 75, Stanford Linear Accelerator Center, Stanford, Calif., USA (1970); Adv. Part. Phys. 1 (1968) 71. 5) K. L. Brown, in Proc. of the Third Int. Conf. on Magnet technology, DESY, Hamburg (1970).
28
TH. WALCHER et al.
6) K. L. Brown and S. K. Howry, SLAC-report no. 91, Stanford Linear Accelerator Center, Stanford, Calif., USA (1970). 7) F. Gudden, G. Fricke, H.-G. Clerc and P. Brix, Z. Phys. 181 (1964) 453. 8) I. Borchardt and K. Steffen, in DESY-Handbuch, Deutsches Elektronen Synchrotron, Hamburg (1965). 9) K. Steffen, High Energy Beam Optics (Interscience Pub., New York, 1965). 10) A. Schwierczinski, Diplomarbeit, Institut f~ir Kernphysik, Technische Hochschule Darmstadt (1971) unpublished. ll) S. B. Kowalski and H. A. Enge, in Proc. Fourth Int. Conf. on Magnet Technology, New York (1972) USAEC-report no. CONF-720908 (1972). J2) H. Ikegami, Rev. Sci. Instr. 29 (1958) 943. 13) S. Penner and J. W. Lightbody, in Proc. of the Int. Symp. on Magnet Technology, Stanford (1965) eds. H. Brechna and H. S. Gordon, USAEC-report no. CONF-650922. 14) C. W. De Jager, F. Th. Couma, P. J. T. Bruinsma and C. De Vries, Nucl. Instr. and Meth. 74 (1969) 13. 15) G. R. Hogg, A. G. Slight, T. E. Drake A. Johnston and G. R. Bishop, Nucl. Instr. and Meth. 101 (1972) 203. ~6) M. Kimura, Y. Torizuka, K. Shoda, M. Sugawara, T. Saito, M. Oyamada, K. Nakahara, K. ltoh, K. Sugiyama, M. Gotoh, K. Miyashita and K. Kurahashi, Nucl. Instr. and Meth. 95 (1971) 403. 17) H. Wi.impelmann and K. Steffen, in DESY-Handbuch,
Deutsches Elektronen Synchrotron, Hamburg (1965). 18) R. Frey, Diplomarbeit, lnstitut ftir Kernphysik, Technische Hochschule Darmstadt (1971) unpublished. 19) j. E. Spencer and H. A. Enge, Nucl. Instr. and Meth. 49 (1967) 191. 20) H. A. Enge and S. B. Kowalski, in Proc. of the Third Int. Conf. on Magnet Technology, DESY, Hamburg (1970). 2t) H. U. Diinnebeil, Diplomarbeit, Institut ftir Kernphysik, Technische Hochschule Darmstadt (1973) unpublished. 22) K. Halbach, Engineering Note, Lawrence Radiation Laboratory, Univ. of Calif. (1972) unpublished. 23) j. K. Cobb and J. J. Murray, Nucl. Instr. and Meth. 46 (1967) 99. 24) H. A. Enge, Rev. Sci. Instr. 35 (1965) 278. 25) H. A. Enge, Nucl. Instr. and Meth. 28 (1964) 119. 26) R. Neuhausen and H. Fricke, private communication. 27) j. S. Colonias and J. H. Dorst. Lawrence Radiation Laboratory, Univ. of Calif., report no. 16382 (1965). 28) A. M. Winslow, J. Comp. Phys. I (1967) 149. 29) A. Rudert, Diplornarbeit, Institut fiJr Kernphysik, Technische Hochschule Darmstadt, (1973) unpublished. 30) j. Foh, Laborbericht, lnstitut fiJr Kernphysik, Technische Hochschule Darmstadt, (1974) unpublished. 31) Th. Walcher, R. Frey, H. D. Graf, H. Miska, D. Schi.ill, E. Spamer, H. Theissen and O. Titze, Proc. of the Int. Conf. on Nuclear Physics, Mtinchen 1973, vol. I (eds. J. de Boer and H. J. Mang, North-Holland, Amsterdam, 1973).
INSTRUMENTS
AND METHODS
153 ( 1 9 7 8 )
17-28;
©
NORTH-HOLLAND
PUBLISHING
CO.
H I G H R E S O L U T I O N E L E C T R O N S C A T T E R I N G FACILITY AT T H E D A R M S T A D T LINEAR A C C E L E R A T O R (DALINAC) * II. BEAM T R A N S P O R T S Y S T E M AND S P E C T R O M E T E R (ENERGY-LOSS SYSTEM) TH. WALCHER*, R. FREY, H.-D. GRAF, E. SPAMER and H. THEISSEN**
Institut .fur Kernphysik, Technische Hochschule Darmstadt, 61 Darmstadt, West Germany
Received 22 November 1977 Design and installation of a high resolution energy-loss electron scattering system at the Darmstadt linear accelerator are described. The apparatus consists of a beam transport system with two 70°-dipole bending magnets, eleven quadrupole focussing
magnets, a five quadrupole magnet set as rotating element, and a magic angle (169.7°) spectrometerfor analyzing the scattered electrons. For a primary momentum spread Ap/po = 3 x 10-3 , a spectrometer acceptance solid angle 0 = 5 msr, and a 10 mg/cm 2 thick Be target, the Tesolution was measured to be 6p/p o = 4x 10 - 4 , equivalent to 25 keV for 60 MeV electrons.
1. Introduction This article is the second of a series of four papers about the new high resolution electron scattering system at Darmstadt. Article 11) dealt with improvements of accelerator (injector and RF driver) and v a c u u m system. In this paper design and installation of beam transport system and spectrometer are described. A conventional electron scattering apparatus with an achromatic beam transport and analyzing system has the disadvantage that a sizable portion of the beam current is lost in the analyzing system where the m o m e n t u m spread of the primary beam is cut down to a value compatible with the desired overall resolution. The D A L I N A C m o m e n t u m spread, for instance, is of the order of A p / p o - ~ 3 x l O -3 (fwhm, see I), about ten times larger than the desired resolution @ / p ~ 3 x 10 4, so that only one tenth of the accelerator beam current could be used in a high resolution experiment. Since high resolution experiments, in any case, suffer from low counting rates due to target thickness limitations imposed by energy straggling, severe reductions in beam current are not tolerable. The possibilities to improve on the D A L I N A C m o m e n t u m spread are limited (see I). For this reason, the " e n e r g y - l o s s " - or "dispersion matching" - m e t h o d (e.g. see ref. 2, 3) was employed. t
Supported by the Bundesministerium for wissenschaflliche Forschung and the Deutsche Forschungsgemeinschaft. * Now at: Max-Planck-Institut ftir Kernphysik, Heidelberg. ** Now at: Gymnasium Mt~nchen-Gladbach-Odenkirchen, Mt~nchen-Gladbach.
Its basic principle is to match the dispersion of the beam transport system to that of the spectrometer such that the entire apparatus (starting at the accelerator exit) is non-dispersive in the spectrometer focal plane. This makes the system sensitive only to the energy loss in the target and not to the m o m e n t u m spread of the beam hitting the target. As a consequence, m o m e n t u m analyzing slits in the beam transport system are not required, so that beam currents comparable to those obtained with conventional systems of moderate resolution are usable. Target thicknesses, however, are limited, due to energy straggling, as in the conventional case. More stringent than in the conventional mode of operation are the requirements for accelerator stability and target uniformity. The reason is the dispersion of the beam on the target, stretching the beam spot out into a strip. The notation used in this article is consistent with that of Brown 4'5) and the one used in code T R A N S P O R T 6) which has been employed in most of the ion-optical calculations.
2. Beam transport system Fig. 1 of I shows the ground plan of the Darmstadt accelerator building. Analyzing system AS1, quadrupoles Q~, Q2 and the 120° spectrometer (120°-Sp.) are elements of the old electron scattering systemT). The switch to the new system is the 70°-dipole magnet M1 downstream of Q~ and Q2. Together with the other 70°-dipole magnet M2 and the six quadrupoles D1, S1 and $2, D2 it forms a second m o m e n t u m analyzing system with slits ES2 in the s y m m e t r y plane between M1 and M2. The rotator R, a set of five quadrupoles, is
18
TH. W A L C H E R et al.
used to turn the dispersion plane in the energy loss mode of operation, and the quadrupole triplett T focusses the beam onto the target. A quadrupole doublet behind the target reduces the beam divergence due to multiple scattering and delivers it to a Faraday cup which simultaneously serves as current monitor. The scattered electrons are momentum analyzed in a high resolution "magic angle" spectrometer (169°-Sp.). Design and arrangement of the new high resolution system were determined by the free space in the building and the condition that the old low resolution system should be further operable. Although designed as an energy-loss system, the new scattering apparatus may also be operated conventionally. In this case, the quadrupoles D1, M1 I
I
D1
$1
IlU
U
S2 D2 U ULI
S1 and $2, D2 are powered symmetrically such that the system is achromatic. Fig. 1 shows the characteristic trajectories for this mode of operation. They were computed on the DESY analogue computer8,9). Assuming an incident beam parallel to the optical axis (emittance e = 0), trajectory Cx = (xlx), is representative. This trajectory intersects, as fig. 1 shows, the optical axis at three points, viz. between M1 and D1, between S1 and $2, and between D2 and M2. All three points are focal points with non-zero dispersion Dx--(xl6). The momentum defining slits ES2 are installed at the focal point between S1 and $2, which coincides with the symmetry plane of the system. At this position, D~ has its maximum value 4.89 cm/% and, as required for an achromatic sys-
M2 I
T1 UUU
I
1.0t x/cm Dx
15 7
~
.
20
Cx -05-
-1.0-
Y/cm
1.0
Cy
0.55 I
\
20 ',
Sy -Q5- 1.0-
Fig. 1. Characteristic trajectories in the convetional mode of operation. - 0 . 1 % . D x ; 1.1 c m . C y ; and 0.75 mrad.Sy.
The
curves
represent
0.25cm.Cx;
2 mrad-S x ;
19
HIGH RESOLUTION ELECTRON S C A T T E R I N G F A C I L I T Y II TABLE 1
Matrix elements of 0" measured upstream of quadrupole doublet Ql Q2 for 90% of total beam current. Accuracy about ___20%. PG: Pierce gun, Hl: Haimson Injector.
Injector
E
v' (711
v' 0 22
0.21
8x
v o33
v' 0-44
0.43
8y
(MeV)
(cm)
(mrad)
(cm mrad)
(cm mrad)
(cm)
(mrad)
(cm mrad)
(cm mrad)
60 50 50 40
0.20 0.25 0.18 0.37
0.20 0.20 0.32 0.30
0.007 0.022 0.041 0.020
0.039 0.047 0.038 0.110
0.38 0.42 0.26 0.44
0.68 0.70 0.23 0.69
0.26 0.29 0.06 0.29
0.023 0.041 0.017 0.100
PG PG H1 PG
tern, is parallel to the optical axis. Additional slits at the two other focal points serve to reduce the beam halo. In order to study the imaging properties of the system for non-zero emittance (s:~0), the emittance of the DALINAC beam was determined 1°) by measuring beam profiles before and after quadrupole doublet Q1 Q2. From these data and the known transformation matrix of the doublet, matrix elements of the beam matrix a were calculated. The beam profiles were determined by counting fission product tracks in mica resulting from electrofission on Bi. The beam diameter was defined as the width of the distribution at 1/5 of the maximum (equivalent to about 90% of the total current). Table 1 contains the matrix elements of crx and try obtained in this way for a position just upstream of quadrupole doublet Q1 Q2. Data were taken for three representative energies and two l
types of injectors, the old Pierce-typ one (now out of use) and the new grid-controlled gun (see I). The measured beam emittances were used to calculate, by means of code TRANSPORT6), the trajectory envelopes displayed in fig. 2. It is seen that the incoming beam diverges in y-direction (V/O'44=~-0, see table 1) which is due to the fringe fields of AS1. The doublet Q1 Q2 serves to make it "parallel", i.e. it generates a "bellow" (a21 = a43 = 0). From fig. 2 the resolution of the analyzing system can be estimated as 6p/p = 2 × 1 0 4 (width at 1/5 of maximum). The extension in y-direction of the beam spot on the target is roughly 0.6 mm. This value is sufficiently small for the spectrometer described below. In the energy-loss mode of operation, the beam dispersion on the target has to be matched to that of the spectrometer. Multiplying the transformation matrices of beam transport system (index
x/cm
03-
,/ . . . . .
0.2'
,~
/
0.1'
_jr
v
V
~
¢
v
-...~__
z/m 0.1 ¸ O2 Q3
OA
UUA Q1Q2
i M1
'UU SL1 D1
U $1
SL2
$2
D2 SL3
M2
T
y/cm Fig. 2. Envelopes in the conventional mode of operation calculated for the measured emittance (table 1 : PG, 60 MeV) and dispersion trajectory D x .
20
TH.
WALCHER
BTS) and spectrometer (index SP), and requiring the total dispersion to be zero leads to: (xl6)Brs = - (x[6)sP E° (x[X)sp E o - E x '
(1)
where Eo is the incident electron energy and Ex the nuclear excitation energy (energy loss). The equation is valid for relativistic electrons with E =pc. The margin within which this condition must be fulfilled without appreciable loss in resolution is, for (xlx) p = - 1 , given by:
6p
>
p
ap [1 p-~
Eo-Ex (xl, ).Ts7 Eo
(xl6)sp_]'
(2)
where Ap/po is the primary momentum spread and 6p/p the desired resolution. Apart from meeting condition eq. (1) an energyloss system requires a sufficiently large resolution of the beam transport system at the target. This means that the target beam spot diameter of a monoenergetic component has to be comparable to the one obtained conventionally. Generalizing the considerations for first order momentum resolution of Brown 4'6) smallest resolution R of a beam transport system for an arbitrary beam matrix a is derived as: R = 3p/p = 2e/[~11(0) I 2 + 2cr21(0) 1112 + + a22(0) 12] +1/2 ,
(3)
with:
11 =
f:
Cx(z ) h(z) dr ;
12 =
fo
Sx(z) h(z) az.
In these equations, Cx and Sx are the trajectories (xlx) and (xlO), respectively, h ( r ) = l/p0 is the curvature of the central trajectory, and 0 denotes the entrance and L the exit of the beam transport system. For the beam transport system considered here, 0 stands for the position of the accelerator exit and L for the target position. For a given beam matrix a with emittance e, the integrals I~ and /2 have to be as large as to make R smaller than the desired overall resolution (i.e. R has to be of the order of the spectrometer resolution). For an achromatic system 11 and 12 vanish. Dispersion and resolution of the beam transport system are obtained by powering quadrupoles S1 and $2 asymmetrically. The dispersion generated in this way is horizontal, whereas the spectrometer, due to its upright installation, is dispersive in vertical direction. A vertical installation of the spectrometer is imperative since one needs:
et al.
1) a large range of scattering angles (40°-165°), 2) a good definition of the scattering angle, i.e. a small acceptance angle in the scattering plane, and 3) a large distance between target and detector system (to create space for shielding). For these reasons, the dispersion plane of the incident beam has to be turned through 90° around the optical axis. The device ll) doing this is the rotator (fig. 1 of I), a set of five quadrupoles whose symmetry planes are tilted through 45 ° against normal orientation. Through the rotated symmetry planes, the ordinarily decoupled x- and y-phase spaces are coupled such that, for proper setting of the gradients, the device acts as a fieldfree drift space interchanging x- and y-coordinates. The quadrupole triplet T not only images the beam onto the target but also serves to adjust the dispersion according to eq. (1). This is done by variing the gradients of the two outer quadrupoles of T. The dispersion is adjustable over the range 4 cm/% < (x] 6)BTs< 6 c m / % . For the spectrometer described below and E0 = 60 MeV, this is equivalent to excitation energies between 0 and 20 MeV. Since the resolution is constant down-stream of M2 (h(r)=0) for a fixed optical mode [eq. (3)], variation Of the dispersion changes the beam spot size and hence the line profile in the spectrum. This is of particular importance for low energy accelerators where the ratio Ex/Eo is large. Fig. 3 shows the beam envelopes for the energyloss mode of operation calculated for the measured emittances (table 1: PG, 60 MeV). The beam spot size on the target is seen to be 0 . 8 × 2 . 0 m m 2 yielding a resolution 6p/p=5×lO 4 (width at 1/5 of maximum). For the dispersion on the target 4 c m / % is obtained a value close to that of the spectrometer. The maximum dispersion behind M2 is 10cm/%. For an inner diameter of the beam pipe of 4 cm this yields a maximum possible momentum spread Ap/p = 0.4%. To avoid excessive background some distance between pipe and beam is desired, so that Ap/p is actually limited to 0.2%.
3. Magic-angle spectrometer The type of spectrometer for the new system was selected according to the following criterions: 1) The resolution should be 3× 10 4 for an acceptance solid angle .(2 = 5 msr and a target beam spot size in vertical direction
21
HIGH RESOLUTION ELECTRON S C A T T E R I N G F A C I L I T Y II
0.4!
x Icm ~\
,~D x- 4 . 1 0
Q3"
-4
/
....
0.2'
,"\
I
,~
~
I I ~'~'~
I I I
I \
I
/'~
//--,,_______~\
0.1
/\
5
/~
lo
I~
~ 15
2o
z/m
o
0.2 0.3
/
'
\1
I ale2
M1
SL1 D1
$1
SL2
$2
D2 SL3
M2
~.
/"
I ROTATOR
T
y/cm
Fig. 3. Envelopes in the energy-loss mode of operation calculated for the measured emittance (table 1: PG, 60 MeV) and dispersion trajectory D x .
2 x0 = 0.1 cm. A m o m e n t u m interval of 3% should be accepted. 2) The linear dispersion should be large enough to permit installation of a scintillator detector system. A set of 36 overlapping plastic scintillators (width 6 m m , length 11 m m and thickness 1.5 mm) yielding 69 channels with a spatial resolution of 0.2 cm (see III) was planned. 3) Inexpensiveness was mandatory. Design, construction and installation should not delay other activities of the laboratory. These requirements are met to a high degree by the so-called magic-angle spectrometer. It is a double focussing sector-field spectrometer with a deflection angle z = ~r v'8/3 = 169.7 °. Devised by Ikegami12), it was propagated by Penner and Lightbodye3), who demonstrated its advantage for electron scattering experiments. It is now used in many electron scattering facilities14-16). Instruments with better ion-optical properties, as for instance a splitpole spectrometer2), were not considered because of their high cost. The magnetic field in the spectrometer midplane is described by the usual expansion: By = B o [1 - n(x/ro) + fl(x/ro) 2 - y(x/ro) 3 + ...], (4)
x being the radial distance from the center trajectory and r0 the radius of the center trajectory. Since n = 0.5 is necessary to obtain double focussing, o n l y / / and 7 are optional. To facilitate manufacturing conical pole shoe faces yielding B = 0.25 and 7 = 0 . 1 2 5 were chosen. The deflection angle r = 169.7 °, together with the straight yoke edges at entrance and exit, makes the second order error (xlO2) vanish for all object distances. Error (xl06) is, as usual, eliminated by tilting the focal plane with respect to the center trajectory through the angle or given by: tan cc = - (010) (xl~)/(xlO~), (5) in this case o~-~35 °. Due to this angle, the detector channel width is halvened to 1 ram. Elimination of the aforementioned second order errors ensures satisfactory performance in the conventional mode of operation. It also suffices for the energy loss mode of operation if precautions are taken to reduce the effect of matrix elements (xlx 2) and (xlxO). These errors are important since the target beam spot size (object size) Xo=(X[6)B~sAp/Po is no longer small. The spectrometer described here has an acceptance angle in radial direction 00-~ ___60 mrad, so that even for a m o m e n t u m spread as small as Ap/po= ___0.15% error (xlxO) limits the resolution.
22
TH. WALCHER et al.
TABLE 2 4. Design, construction and test of quadrupoles, Parameters of beam transport system magnets. bending magnets and soectrometer All magnets including power supplies were Quadrupole magnets: 12.00 cm manufactured, according to plans of the Institut Geometric length 12.64 cm for Kernphysik, by Lintott Engineering Ltd., Hor- Effective length 2.75 cm sham, Sussex, England. In the design of the mag- Aperture radius Maximum gradient 1.3 kG/cm nets, special attention was paid to field uniformity Maximum current 20 A of the dipole magnets, small amplitudes of higher Maximum power 240 W air harmonics in the quadrupoles, and, in general, Cooling 118 kg short fringe fields. The quadrupoles (D1, S1, $2, Weight D2, T) are slightly modified reduced size copies of Dipole magnets: the DESY standard construction9,17). Their paRadius of center trajectory 1.00 m rameters are summarized in table 2. Tolerances in Gap width 5.00 cm machining the pole shoe contours were set to Vacuum chamber (inside cross-section) 4.3 × 8.0 cm 18-120 MeV _+0.02 ram. Hyperbolically shaped edges and mir- Energy range 0.6--4.0 kG ror plates at entrance and exit ensured a short and Field strength Maximum current 250 A almost linear fringe field, the shape being inde- Maximum power 6 kW pendent of field strength. For all quadrupoles the Cooling water 1.3 t gradient was measured as a function of distance Weight 70.0° _+0.1 ° along the optical axis. A temperature-stabilized Deflection angle Field uniformity _+ 10 -4 and compensated Hall plate (Siemens SBV 579) Slope of entrance edge MI 25.0°_+0.5 ° with a relative accuracy of _+2×10 -4 (_+0.4G Slope of exit edge M2 minimum) was used as field probe. It was mount- Slope of exit edge M1 0.00_+0.5 ° M2 ed on a lathe tool carriage permitting semi-auto- Slope of entrance edge matic movements in three directions. The measurements yielded an effective length of 126.4 mm for all quadrupoles, the deviation from this aver- mated with the help of TRANSPORT 6) were age value being less than _+0.2 mm. The propor_+0.1 mm. An accurate determination of the magtionality between gradient and exciting current netic axis of each quadrupole was therefore manwas measured to be better than _+10-3 , a value datory. It was carried out after the method of Cobb achieved by giving the quadrupoles a large pole and Murray 23) and yielded accuracies of better basis. The results of the field measurements were than _+0.03 mm~8). The axis coordinates were dealso used as input data for ray-tracing calculations termined relative to two adjustment cross-wires on with the code RAY-TRACINGS9'2°). These calcu- top of the quadrupole yoke. The bending magnets lations and additional floating wire experiments 21) were furnished with identical cross-wires mounted showed that the theoretical first order focal in the same height above the beam line. This falengths were reproduced, for the gradients used cilitated an accurate installation of the entire syshere, to within _+0.3%. As a further test, the tem. quadrupole field was subjected to a harmonic analThe bending magnets M1 and M2 are H-type ysis according to the method of Haibachn). The dipole magnets with one of the two edges (enrelative amplitudes of higher harmonics (multipole trance edge of M1 and exit of M2) sloped by 25 ° field strength divided by quadrupole field strength, for vertical focussing. The pole shoes on both both measured at the aperture radius of 2.75 cm) edges have a threefold bevel approximately formmeasured in this way were less than 2× 10 -4 ex- ing a hyperbola. Together with the mirror plates, cept for a 3% contribution of the duodecapole am- this ensures a short and linearly decreasing fringe plitude (allowed multipole component of lowest field independent of excitation. Displacement and order). slope of the beam (with respect to the center traThe adjustment tolerances of the system esti- jectory) after traversing the magnet are thus expected to be negligible24). Measurements of the fringe field with the aforementioned Hall probe The measurements were kindly performed by Dr. Langenbeck, GSI, Darmstadt. and subsequent ray-tracing calculations confirmed
HIGH
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this2~). The effective field boundary coincided with the geometrical edge to within better than 0.4 m m , so that the effective deflection angle was 70.0°+_0.1 °. Filter gaps 2s) secured a high uniformity of the main field (see below). Measurements with an N M R probe 21) yield a m a x i m u m variation in field strength of ___10 -4 over a range of _+4 cm perpendicular to the beam axis for fields between 0.6 and 4 kG. The pole shoe width, for comparison, is 20 cm. Further parameters and properties of the magnets are listed in table 2. The limitations in resolution due to finite detector system channel width (1 mm) and beam spot diameter on the target ( ~ 1 mm) require a spectrometer with a large radius. A large radius, on the other hand, makes it difficult to shape the field precisely according to eq. (4) since the field strength is small. The reasons are the small permeability and the remanent magnetism at field strengths below 1 kG for normal high grade magnet iron (carbon content <0.07%). As a tolerable compromise, a radius of 1 m was chosen, so that, for fields between 0.6 and 4 kG, electrons with 18 MeV to 120 MeV energy are analyzed. Table 3 lists the main construction parameters of the spectrometer. Since the m a x i m u m field strength used in the experiments is small (2.3 kG for 70 MeV electrons), it was sufficient to close the magnetic flux through the inner part of the sector. The resuiting C-shape yoke has the advantage that the TABLE 3 Parameters of spectrometer. Radius of center trajectory Gap width Vacuum chamber inside cross-section open back Energy range Field strength Maximum current Maximum power Weight spectrometer shielding (safe load) Deflection angle Field coefficients n fl y Object distance Image distance Entrance and exit angle Curvature of pole edges
1.00 m 10.0 cm 7.5 c m × 26 cm 30 ° < cz< 150° 18-120 MeV 0.6-4.0 kG 280 A 25 kW 17 t 10 t 169.6°-+0.1 ° (169.7°-+0.1 °) 0.5036_+0.0023 (0.500) 0.259 _+0.008 (0.250) 0.09_+0.07 (0.125) 0.87 m 0.65 m (0.78 m) 0.0_+0.1 ° (0°) 0 (0)
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spectrometer is iron free on the back. N e u h a u s e n and Fricke 26) have demonstrated that this reduces background in inelastic scattering if, in addition to that, the v a c u u m chamber on this side is sealed with a thin foil. The reason is that backscattering from the chamber walls or other material is reduced. Because of the unusual design of the spectrometer (C-type yoke and low field strengths) the field distribution in iron and gap was calculated with code TRIM27,28). This programm solves, by means of a finite difference method, the vector potential problem for a given relation between permeability and field strength. Fig. 4 shows the cross-section of the magnet with the calculated field lines for a spectrometer with and without filter gap. The effect of the filter gap is clearly visible. The field lines leave the iron less oblique (with respect to the pole shoe planes) than in the case without filter gap. Another advantage is that the field configuration depends only weakly on exciting current. The shims at the pole shoe edges seen in fig. 4 extend the range in radial x-direction over which the field follows eq. (4). The field was measured 29) with a rotating coil instrument ( R a w s o n - L u s h model no. 924/944) of a relative accuracy of +_2×10 -5 and the aforementioned Hall probe which had the same relative accuracy for differential measurements. Data were taken for three deflection angles (65 ° , 87 ° and 119°). Systematic deviations among the results for the three angles were not observed and a dependence of the field pattern on exciting current could not be detected. The mean values of the field coefficient for - 10 c m < x < 10 cm from all measurements were: n = 0.5036_+0.0023, fl = 0.258 _+0.008, ? = 0.09 +0.07. A least squares fit of By according to eq. (4) to the field calculated with TRIM27,28), on the other hand, yielded for the same interval: n = 0.4975, 13 = 0.232, ? = 0.08. The deviation between measurement and calculation could not be fully explained. Insufficient accuracy of the computer code was ruled out since the results were to a high degree independent of the pivotal points. Qualitative agreement with the
24
TH. W A L C H E R et al.
iiiiil IIIIIlll
/ I
i
Fig. 4. Field lines in magic angle spectrometer with and without filter gap.
result of conformal mapping corroborated this. A probable explanation is a local permanent magnetization of the pole shoes at x = - 1 7 cm and + 19 cm caused by magnetic welding seams of the first (stainless steel) vacuum chamber. This chamber was later replaced by a non-magnetic one. The deviations between actual and ideal field coefficients have only minute effects on the spectrometer optics. As the bending magnets, the spectrometer has a threefold, approximately hyperbolic, bevel at the yoke edges and mirror plates in order to linearize the fringe field. The effective field boundary which defines the actual deflection angle deviates by (0.15_+0.05)cm from the geometrical edge of the iron. This yields a deflection angle r = 169.6°_+0.1 °. The field parameters measured for the spectrometer were used to calculate its imaging properties. This was done with code RAY TRAC-
ING 19,2°) modified such that the variation of n in the fringe field was taken into account. The code evaluates, by integrating 44 trajectories, matrix elements of up to fourth order. The result is listed in table 4, column A. For comparison, calculations with RAY TRACING for a constant n in the fringe field and TRANSPORT have been performed, the results being displayed in columns B and C, respectively. In order to reach scattering angles up to 165 ° the object distance (distance between target beam spot and spectrometer effective field boundary) was chosen to be do = 87.0cm. For this do, the first order image distance (distance between spectrometer effective field boundary and intersection of center trajectory with radial focal plane) is calculated to be dlX)= 78.4 cm, whereas RAY TRACING 19'2°) yielded 71.1 cm. The measured image distance (see III) was dlX~= 66.5 cm. An explanation of the discrepancy cannot be given.
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TABLE 4 Transformation matrix elements of magic-angle spectrometer for the focal plane calculated with RAY TRACING19,2°). Units are cm, mrad and %. Power of ten in parentheses. A: measured field with n = 0.5036, /3= 0.2598, y =0.0932, linear fringe field with measured n=n(z), object distance d o = 87.0 cm, image distance d I = 70.8 cm and angle between focal plane and center trajectory ~ = 34.9 °. B: design with n = 0.5,/3 = 0.25, 7 = 0.125, linear fringe field with n = 0.5 over entire range, d o = 87.0 cm, d I = 76.0 cm and ~ = 33.9 °. C : result of calculation with TRANSPORT 6) for comparison, n = 0 . 5 0 3 6 , /3=0.2598, ~=0.0932, linear fringe field with K I = 0.33 ; K2 = 0.0, d o = 87.0 cm, d I = 78.4 cm and ~z= 33.9 °. Matrix element
(xlx) (xl 0) (xl 5) (YlY) (vl 0)
(OIx) (010) (0[6) (OlY) (0[0) (xlx 2)
(xlxO) (x[x6) (x[O 2)
A
-
-
-
(x106) (xly 2)
(xlyO) (xlO 2) (x162) (xlO 3) (xlO02)
(xlxO2) (xlx 2 O)
(x1026) (xt 062) (xlxO 2) (x] 02 6) (x]O4) (x] 02 02) (x10262) (xl 04)
-
-
0.955 0:000 3.760 0.885 0.017 5.606 1.046 10.768 6.785 0.993 7.580(-3) 1.419(-3) 2.961(-2) 1.190(-6) 4.631 ( - 6 ) 1.126(-2) 9.503(-4) 1.480(-4) 6.217(-2) 1.294(-7) 7.183(-7) 1.172(-6) 7.808(-6) 4.778(-6) 1.516 ( - 4 ) 2.115(-6) 1.841 ( - 6 ) 7.165(-11) 1.969 ( - 10) 3.551(-8) 2.878 ( - 10)
Value B
C
0.966 - 0.974 0.000 0.000 3.921 3.977 0.945 - 0.971 0.006 0.000 6.136 - 6.126 1.034 - 1.027 12.225 12.344 6.444 - 6.438 1.013 - 1.027 8.486(-3) 8.430(-3) 1.434(-3) 1.411 ( - 3 ) 3.335(-2) - 3.361(-2) 0.000 - 2.656(-6) 2.536 ( - 4 ) 2.403 ( - 4 ) 1.211(-2) - 1.185(-2) 9.492(-4) - 9.101(-4) 1.470(-4) - 1.347(-4) 7.210(-2) 7.283(-2) 8.706(-8) 5.315(-7) 8.562(-7) 6.474(-6) 3.394(-6) 1.991 ( - 4 ) 1.862(-6) 3.938 ( - 7 ) 8.631(-11) 3.865 ( - 10) 7.433(-8) 2.480 ( - 10)
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The angle cz between focal plane and center trajectory depends mainly on /3 and is insensitive to variations of the fringe field gradient. From table 4 one obtains ~ = 350___0.5°. The transformation matrix elements (table 4) supplied by RAY TRACING 19,2°) were finally used to calculate the intrinsic resolution of the spectrometer. Initial coordinates of about 105 particles uniformly distributed over the phase space given by beam spot size, spectrometer acceptance solid angle, etc. were therefore transformed into the focal plane. For the conventional mode of operation, the phase space contour was taken to be x 0 = 0 , Y0=+-0.1cm, 00= + 6 0 m r a d , and 00 = ___18 mrad, equivalent to a monochromatic line source and an acceptance solid angle of 4.3 msr. For the energyqoss mode of operation, a source with x0= +_0.5cm, corresponding to Ap/po= +_0.13% (the monoenergetic spot size is zero), and otherwise same parameters was assumed. All matrix elements up to fourth order were taken into account. The result is shown in fig. 5. It is seen that the line widths (fwhm), for a momentum range of _1.5%, are smaller than 1 . 5 X 1 0 - 4 . Since the contributions of detector width and beam spot size a r e 3 x l 0 -4 and ,
10
,
r
,
i
,
,
f
,
6 = 0,0%
~
ZI;K <11<3
'
=/,
,
conventional
-1.5%
i
* 1.5°1°
1.2'10 -4
' . . . . . . . energy 8=0.0,1,
1 4 10 4
,
mode
1.2"10 4
'
, ' ' loss mode
1.4.10 4
.4.10.4
5
Radial image distance dl ~) and axial image distance dl y) are interrelated. For the difference dlY)-dl x)= --(Ylq~)/(q~lq~) one obtains 17 cm. For an acceptance angle 00 = ___20 mrad this astigmatism causes an axial image width of 9 mm in the focal plane. Since the scintillation counter of the detector system are 11 mm wide in y-direction, the angle 00 had to be reduced to ± 15 mrad to avoid fluctuations in counting rate due to drifts of the target beam spot position (see III).
_55-s5"'-o.~o'.o61
'~'' 5.7
5:9
x/cm
Fig. 5. Upper part: intrinsic line profile for the conventional mode of operation in the focal plane caused by spectrometer aberration errors up to fourth order. Line source with phase space boundaries x 0 = 0 , Yo = _+0.1 cm, 00 = _+60 mrad, and 0o = _+18 mrad; x is the distance to the center trajectory; 5 denotes the relative m o m e n t u m difference. Lower part: same for the energy-loss mode of operation, x 0 = 0.5 cm, equivalent to Ap/p o =_+0.13% (see text), Y0, eo and 00 as before.
26
TH. W A L C H E R et al.
TABLE 5 Imaging properties of magic angle spectrometer. Maximum radial acceptance angle 00max Maximum axial acceptance angle O0max Maximum solid acceptance angle 3"2max Dispersion Momentum interval accepted Resolution (point source, fwhm) Tilt of focal plane
_+75 mrad ± 2 0 mrad 6 msr 3.76 c m / % _+ 1.5% 0.015% 35 °
2 x 10 4, respectively, this is tolerable. The imaging properties of the spectrometer are summarized in table 5. The spectrometer rests on a 360 ° turntable whose height is adjusted by 84 screws. The maxi m u m deviation of the rotation axis from its mean position was measured to be 0.2 m m , the angle between spectrometer s y m m e t r y plane and axis of rotation to less than _+0.3 mrad. The scattering chamber is a modified version of the construction described by G u d d e n e t al.7). Borings at 12 ° intervals and auxiliary flanges permit the spectrometer to be set to 13 scattering angles between 57 ° and 165 ° . The power supplies are current stabilized with a (short and long time) stability of ± 2 x 10 5 for the dipole and _+10 4 for the quadrupole magnets. Each unit has a digital-to-analogue converter (DAC) with a resolution of 10 5 and a stability of _+2 × 10 6 as reference source. The reference voltage is remotely controlled in the analogue branch. All D A C ' s are linked to a digital master set which allows simultaneous stepping up or down of relative settings. The system may thus be quickly adjusted to changes in electron energy leaving only small corrections to be done by hand. The spectrometer power supply obtains its reference signal from a rotating coil which measures the field strength. The control unit of the rotating coil was modified 3°) such that it automatically locks on the digitally given field strength.
5. lon-optical test T h e beam is threaded through the magnet system with the help of two pairs of Helmholtz coils, one upstream of Q1 Q2, the other between M2 and the R O T A T O R . To determine the beam intensity profile at the target position, a tantalum wire (diameter 0.1 ram) was swept up and down through the beam and the secondary electron current measured as a function o f wire position. Fig. 6 shows
Fig. 6. Beam intensity on the target as a function of distance in vertical direction. Upper part: conventional mode of operation. Middle part: five beam spots in the energy-loss mode of operation, slit width of analyzing system (ES2, fig. 1 of I) 3p/p o - 2 x 10 -4. Slit positions 3p/p o - ± 0 . 1 % , _+0.05% and 0% (see text). Lower part: dispersive beam spot for a primary width of 3P/Po~ _+0.1%. Scale factor 1.25 cm/div.
HIGH R E S O L U T I O N
ELECTRON
the result. In the conventional mode of operation the beam spot is seen to be 0.8 mm wide (upper part of fig. 6). The intensity distributions of the monoenergetic component in the energy loss mode of operation (middle part of fig. 6) were obtained with the momentum defining slits ES2 (fig. 1 ofI)being open to Ap/po = 2 x 10 -4 and setting them together in parallel to Ap/po = 0 , -+-5.10 4 and ±10 3. For a dispersion of 4 c m / % on the target, the lines are expected at x = 0, ±2 and ± 4 mm. From fig. 6 one obtains x = - 3 . 9 , - 2 . 0 , 0.1, 2.1 and 4 . 2 m m with art error of about ±0.1 mm. The dispersion (xl6)sp = (4.1 ±0.1) cm/% following from these values is, according to eq. (2), sufficiently accurate. The line width (~ 1.3 mm) is about 40% smaller than calculated with the measured emittances. If the broadening (x/6)aTsAp/Po= 0.8 mm due to dispersion is taken into account, the line width of the monoenergetic component in the energy loss mode of operation is comparable to that of the conventional mode. The lower part of fig. 6 shows the dispersed beam spot obtained with the slits ES2 opened to ±10 -3. To test the over-all resolution of spectrometer and beam transport system3~), a single plastic scintillator with a width of 1 mm was mounted in the spectrometer focal plane and the line widths of electrons scattered elastically from a 11 mg/cm 2 thick Be target were measured. The result is shown in fig. 7 where the halfwidths (fwhm) 6p/p of the elastic peak have been plotted as a function of slit width Ap/p o of the analyzing system. The acceptance solid angle of the spectrometer was ,Q = 4.8 msr (20o = 120 mrad, 2~0 = 40 mrad) in this measurement. In the conventional mode of 30
i
i
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operation the resolution, as expected, increases, from a initial value of 3.7x 10 4, proportional to Ap/po. Since the intensity of the primary beam transmitted through the slits is not constant (fig. 6, lower part), 6p/po is even smaller than 3p/po. In the energy loss mode of operation the resolution is constant and has the value 4.2× 10 -4. In the conventional mode of operation, the peak half width comprises the contribution of beam spot size (1.2 × 10-4), spectrometer intrinsic resolution (1.2× 10-4), detector width (3x 10 4) and energy spread Ap/po of the primary beam. For Ap/po = 1.5 × 10 -4, for example, the quadratic sum of all contributions is 6p/po = 3.8× 10 4, in agreement with the value obtained from fig. 7. In the energy loss mode of operation the beam spot size contributes !.9× 10 4, the spectrometer 1.4× 10 4 and the detector width, as before, 3× 10 4. Since the energy spread of the primary beam does not enter, one obtains 6p/po = 3.8× 10 -4. The discrepancy between this value and the measured one is probably due to an under estimate of the different contributions (see III). 6. Conclusion The apparatus described in this article is the first electron scattering energy-loss system set into operation. Its overall resolution was measured to be 4× 10 4 for a thin target. Since a primary momentum spread of up. to 0.3% is permissible, a great fraction of the accelerator current (--~25 ~A) may be used.
It has been demonstrated that the energy-loss principle may be successfully employed to increase the resolution of electron scattering experiments without appreciable reduction in beam intensity.
i
; ?; oot,ooo, modo References ,~ 20 0 )< o tn [D_ ~o
10
I
0
10
2'0
3'0
Ap/PoXl04 Fig. 7. Resolution 6p/p measured with a single counter as function of primary width Ap/p o.
l) H.-D. Gr~if, H. Miska, E. Spamer, O. Titze and Th. Walcher, Nucl. Instr. and Meth. preceding article. 2) S. B. Kowalski, W. Bertozzi and C. F. Sargent, in Medium energy nuclear physics with electron linear accelerators, MIT 1967 Summer Study, ed. W. Bertozzi and S. Kowalski, USAEC report no. TID-24667 (1967). 3) S. B. Kowalski, in Proc of the Int. Conf. on Photonuclear reactions and applications, Asilomar (1973) Calif., USA, ed. B. L. Berman, USAEC report no. CONT-730301. 4) K. L. Brown, SLAC-report no. 75, Stanford Linear Accelerator Center, Stanford, Calif., USA (1970); Adv. Part. Phys. 1 (1968) 71. 5) K. L. Brown, in Proc. of the Third Int. Conf. on Magnet technology, DESY, Hamburg (1970).
28
TH. WALCHER et al.
6) K. L. Brown and S. K. Howry, SLAC-report no. 91, Stanford Linear Accelerator Center, Stanford, Calif., USA (1970). 7) F. Gudden, G. Fricke, H.-G. Clerc and P. Brix, Z. Phys. 181 (1964) 453. 8) I. Borchardt and K. Steffen, in DESY-Handbuch, Deutsches Elektronen Synchrotron, Hamburg (1965). 9) K. Steffen, High Energy Beam Optics (Interscience Pub., New York, 1965). 10) A. Schwierczinski, Diplomarbeit, Institut f~ir Kernphysik, Technische Hochschule Darmstadt (1971) unpublished. ll) S. B. Kowalski and H. A. Enge, in Proc. Fourth Int. Conf. on Magnet Technology, New York (1972) USAEC-report no. CONF-720908 (1972). J2) H. Ikegami, Rev. Sci. Instr. 29 (1958) 943. 13) S. Penner and J. W. Lightbody, in Proc. of the Int. Symp. on Magnet Technology, Stanford (1965) eds. H. Brechna and H. S. Gordon, USAEC-report no. CONF-650922. 14) C. W. De Jager, F. Th. Couma, P. J. T. Bruinsma and C. De Vries, Nucl. Instr. and Meth. 74 (1969) 13. 15) G. R. Hogg, A. G. Slight, T. E. Drake A. Johnston and G. R. Bishop, Nucl. Instr. and Meth. 101 (1972) 203. ~6) M. Kimura, Y. Torizuka, K. Shoda, M. Sugawara, T. Saito, M. Oyamada, K. Nakahara, K. ltoh, K. Sugiyama, M. Gotoh, K. Miyashita and K. Kurahashi, Nucl. Instr. and Meth. 95 (1971) 403. 17) H. Wi.impelmann and K. Steffen, in DESY-Handbuch,
Deutsches Elektronen Synchrotron, Hamburg (1965). 18) R. Frey, Diplomarbeit, lnstitut ftir Kernphysik, Technische Hochschule Darmstadt (1971) unpublished. 19) j. E. Spencer and H. A. Enge, Nucl. Instr. and Meth. 49 (1967) 191. 20) H. A. Enge and S. B. Kowalski, in Proc. of the Third Int. Conf. on Magnet Technology, DESY, Hamburg (1970). 2t) H. U. Diinnebeil, Diplomarbeit, Institut ftir Kernphysik, Technische Hochschule Darmstadt (1973) unpublished. 22) K. Halbach, Engineering Note, Lawrence Radiation Laboratory, Univ. of Calif. (1972) unpublished. 23) j. K. Cobb and J. J. Murray, Nucl. Instr. and Meth. 46 (1967) 99. 24) H. A. Enge, Rev. Sci. Instr. 35 (1965) 278. 25) H. A. Enge, Nucl. Instr. and Meth. 28 (1964) 119. 26) R. Neuhausen and H. Fricke, private communication. 27) j. S. Colonias and J. H. Dorst. Lawrence Radiation Laboratory, Univ. of Calif., report no. 16382 (1965). 28) A. M. Winslow, J. Comp. Phys. I (1967) 149. 29) A. Rudert, Diplornarbeit, Institut fiJr Kernphysik, Technische Hochschule Darmstadt, (1973) unpublished. 30) j. Foh, Laborbericht, lnstitut fiJr Kernphysik, Technische Hochschule Darmstadt, (1974) unpublished. 31) Th. Walcher, R. Frey, H. D. Graf, H. Miska, D. Schi.ill, E. Spamer, H. Theissen and O. Titze, Proc. of the Int. Conf. on Nuclear Physics, Mtinchen 1973, vol. I (eds. J. de Boer and H. J. Mang, North-Holland, Amsterdam, 1973).