A new position measurement for ionization chambers

Nuclear Instruments and Methods 188 ( 1981) 561-569 North-Holland Publishing Company

561

A NEW POSITION MEASUREMENT FOR IONIZATION CHAMBERS

G. ROSNER, B. HECK, J. POCHODZALLA, G. HLAWATSCH, B. KOLB and A. MICZAIKA Max-Planek-Institut far Kernphysik, Postfach 103980, D-6900 Heidelberg, FR G

Received 31 March 1981

A new method has been applied for measuring the second position coordinate of particles detected in an ionization chamber. The position is determined by geometrically dividing the charge on the first zXEanode. The resolution obtained was 0.3 mm. The energy, energy loss, and time resolution of the time-of-flight spectrometer (ionization chamber plus parallel plate avalanche counter) were ~E/E = 0.3%, 6 zXE/zaE= 3%, At = 150 ps for 142 MeV 32S ions. 1. Introduction Precise position measurements over a wide dynamic range have become necessary for detecting heavy ion reaction products using large area counters. Conventionally, one coordinate of an ionization chamber (IC) is determined by the drift time of the electrons to the Frisch grid. The other coordinate is much more difficult to measure. Several methods have been applied. A position-sensitive proportional counter between the &E anodes [1,2] can be used. This deteriorates the energy resolution. An additional "0 grid" between the Frisch grid and the anode plate [3] degrades the energy resolution and limits the counting rate. A position-sensitive parallel plate avalanche counter (PPAC) in front of the IC [4] causes straggling at the narrowly spaced wires of the electrode grid. This becomes crucial at higher incident energies. Another technique has been applied for X-ray detection with proportional counters [5]. Here, the position signal was derived from a split cathode. Since determining the position essentially by geometrical means seems very simple, we cut the first zXE anode of an IC into adequately formed segments. We report on the position resolution and linearity of such a device and its consequences with respect to energy, energy loss, and time resolution.

pendicular to the flight direction, can be related to a measurement of partial energy losses along the parti-

cle track. The total energy loss across the zXE anode is distributed among the left and right parts of the position-sensitive anode (PSA) according to Yl. The segmented z2xE anode has a trapezoidal form to account for the opening angle 2ao of the IC. The special geometry o f two opposite saw-blades showed the best linearity (see section 3.2). Defining stripes o f constant depth d = ril + l i + ri2 = r i + li, the energy loss across one stripe is divided into a left and a right

2. Position measurement 2.1. General description

The basic design of a segmented z2~E anode is shown in fig. 1. The position Y l, approximately per0029-554X/81/0000-0000/$02.50 © 1981 North-Holland

Fig. 1. Schematic diagram of the position-sensitive anode.

562

G. Rosner et al. / A new position measurement

signal according t o lilt i. The left and right parts of the stripes are connected, yielding the signals E L and ER, respectively. The quantity y

ER - EL =

-

ER

-

grid. Since we wanted to measure the positions by using only the IC, we did not apply the better START signal of the PPAC. The y coordinate was calculated on-line according to eq. (1).

(1)

+EL

is proportional to the particle position Yl, which relates to the angle ~ or the scattering angle, y depends linearly on Yl only if the particle is not stopped on the PSA (cf. section 3.2). 2.2. Experimental setup

The measurements were performed with a modified version of the chamber described in ref. 4. It consists of an IC behind a PPAC. The PPAC consists of two polypropylene foils (35 #g/cm 2 thick, with an area of 6 × 6 cm 2) with thin gold evaporated layers. The foils are 2 mm apart. The PPAC operates with isobutane at 5 Torr; the voltage applied was 580 V. The anode of the IC is made of 3 mm thick epoxy with a 3 5 / l m copper layer and is divided into three sections with lengths of 12, 9, and 65 cm. The entrance window covers about 4.5 cm of the first AE anode, which has a width of 2bl = 8 cm. The first zSa~anode represents the position-sensitive, segmented part of the anode. Several PSA with different numbers n of stripes have been tested. Potential wires, which also run over the entrance window as a supporting grid, keep the electric field homogeneous at the position of the PSA. The sensitive volume of the IC is completely shielded against the walls by potential dividers along the sides of the chamber. The IC operates with an argon : methane mixture (90 : 10) at 80 Torr. The cathode voltage was - 2 4 0 V, the anode voltage 60 V. The signal of the PPAC was fed into a fast timing amplifier (FTA, amplification factor 200), a constantfraction discriminator (CFD), and a time-to-digital converter (TDC) as the STOP signal. The START signal was delivered by a rebuncher-micropulsing system [6]. • The anode signals of the IC were preamplified and amplified with a shaping constant of 1/~s. The sum of the signals E L and ER of the PSA was fed into a zerocrossing trigger and stopped a time-to-amplitude converter (TAC). This TAC was started by the cathode signal via preamplifier, timing-filter amplifier, and leading edge discriminator (LED). Thus, the x coordinate was determined by measuring the drift time of the electrons from the particle track to the Frisch

3. Results 3.1. Position resolution

The two-dimensional position resolution of the IC was tested using a collimator with 0.5 mm diameter apertures. The position-sensitive A~? anode, in this experiment, consisted of 12 stripes with depth d = 10 ram. Fig. 2 shows an image of the collimator caused by elastically scattered 142 MeV 32S ions. The position resolutions are satisfactory over the full entrance window. The x resolution is limited to 5x ~ 1 mm due to the time resolution of the cathode LED signal. It becomes significantly better with the PPAC signal used as the START signal for the drift-time TAC. The resolution and linearity of the y coordinate measured by the PSA are quite good, as can be seen quantitatively from fig. 3. Several PSA have been tested. Keeping the width (261 = 80 mm) and the total depth (120 mm) constant, the number n or the depth d of the stripes has been varied from n = 2 , d = 6 0 m m to n = 2 4 , d = 5 ram. The left side of fig. 4 displays the resulting experimental position resolutions 6YEx o as a function o f y . The trivial contribution of the aperture (r = 0.25

I

~

I

'

I

+ 20

n

I

i

I

~

I

'

I

;

.~,-

-~

'~"

O

E v >, - 10

,~t-

"41~

~l

-20

!

~

-30

-20

-10

i

0

+10

+20

.,'.30

x (mm)

Fig. 2. Image of a collimator (apertures with spacing 5 or 10 mm, diameter 0.5 mm), taken with elastically scattered 142 MeV 325 and high statistics. The entrance window of the IC had an aperture of 50 mm. The x coordinate was measured by the drift time method, the y coordinate by the positionsensitive anode.

G. Rosner et al. / A new position measurement 200

I

I

'

I

I

I

'

I

I

563

As usual, the average of some quantity with respect to a particle ensemble is denoted by

. (fp) stands for the actual deviation (fp) = p -

; the variance 62p is defined as 62p =<(p _. The

'

{n

(62p)U2.

standard deviation 6 p equals

100

Since expressions with averages (EL> , are much easier to handle than formulae with ER or E L, we note

o

I -20

r

-10

I

i-

0

+10

'

I

=

÷20

+

~ +
(2)

y(mm)

This can be seen from a series expansion of <(ER Fig. 3. Position resolution and finearity of the position-sensitive anode (aperture spacing 5 mm, diameter 0.5 mm).

EL)/(ER +EL)). Experimentally, (y> correspond to

mm) to the width of the position peaks has been quadratically subtracted (fy~×p = 6Y~'eak -- 3r2) . Two features of the experimental points in fig. 4 should be noted. First, the resolutions 6YExp are clearly dependent on the position y for the deep stripes with d = 60 and 30 mm. Second, the finer the segmentation of the PSA, the better the mean resolution down to 6yEx p = 0.33 mm for d = 10 mm (cf. table 1). However, it gets worse again for d = 5 ram. In order to explain the dependence of the position resolution on the depth d, we assume the resolution to be essentially limited by two factors. Naturally, one contribution is the noise of the electronics; the other is the energy loss straggling across the PSA.

6~y =((iv _

the maxima of the peaks in fig. 3. A further series expansion then yields

1

(~

)2>

[(1 - )2 fZER + (1 + )2 f2EL

-- 2(1 -- 2) 76ER fEL] .

Quantities of the order higher than or equal to (fiE/ )4 have been neglected. (5E/ is defined as
<(fER)(fEL)> -

(4)

6ER f E L

The standard deviations 6ER, fiE[. and the correlation'

1.5

1.5 (~)l (~& ,D

®o

®.

--- l ,

/ I"

1.0

d =60ram = 30ram = 10 mrn = 5ram

I

/

•

7

~

~

1.0

/" /"

\.

/

N

(~ /"

~o

X',,

0.5

3.5

®.--~

0 -30

I

1 -20

I

I -10

I

I 0

I

1 10

I

I 20

i

y (ram)

,

I -20

(3)

,

I -10

i

I 0

,

I 10

I

I 20

n

0 30

Fig. 4. Experimental (left) and theoretical (right) position resolutions 6y (fwhm) for anodes no. 1 to 4.

G. Rosner et al. / A new position measurement

564

coefficient 3' will be calculated separately with respect to energy loss straggling and electronic noise. First, the contribution of the energy loss straggling is estimated. In a simple model (for details see Appendix), we calculate the individual contributions of the energy loss straggling across one stripe. These energy loss stragglings are then mixed by diffusion of the electrons drifting from the particle track to the PSA. The main result of the model is that the diffusion process strongly correlates a left segment of the PSA to neighboring right ones, thus decreasing the energy loss straggling across this segment and giving rise to a large correlation coefficient 3' > 0. Since (y) c [ - 1 , 1], 62y decreases. Actually, 62Ystr ~ 0 , if the mixing of the energy loss stragglings across two neighboring segments is complete. This will happen for sufficiently fine segmentation of the PSA. According to the derivation given in the Appendix, 62Estr

(l+yo 2

o ) d(fo)

~2Estr'L = 62Estr

(1-yo 2

o) d(yo)

62Estr'R =

(5)

"

(6)

Yo denotes the normalized, geometrical position Yo = J'l/bl ~ [ - 1 , 1], d(yo) the actual depth [eq. (A10)]. The rms energy loss straggling ~Est r across the full PSA is estimated [7] to be 62Estr =c'K(E) •

(7)

The proportional factor 9( is estimated [4] to be CK(MeV) ~ 1.563 X 10 4

ZT

+ k2Zp

(8)

with: Zp the nuclear charge number of the projectile (e.g., 32 16S),. ZT, AT the charge and mass number of the target (e.g., '~°Ar); Sp(v) the proton stopping power (MeV cm2/mg); v the projectile velocity (MeV/u); k = kargon = 0.011 MeV 1/2. For the diffusion length in eqs. (5) and (6) we note the common ansatz (9)

It is: x = 9.2 cm the drift length to the PSA; 6 = 17.5 V/cm, the electric field strength; D/IJ = 0.26 V the drift coefficiont D over the electron mobility ]1 from ref. 8 ; consequently, o = 5.2 mm for our chamber. The correlation coefficient 3'str reads =

duo)

-

2 r = ~cK ( 1 - y ~ 6Yst

- ~ 40 -(1

+ y g t a n 2 a o ) -1/2 ) . (11)

According to eq. (11), the limiting case of full mixing, i.e., no contribution to the position resolution from energy loss straggling, holds for d~<(l_yg)(1

40 +y2otan2ao) 1/2 "

(12)

In our experiment, this will happen at Yo = 0 for d ~< 4o = 20.8 ram, for example. Therefore, the position resolutions 6YExp in fig. 4 originate exclusively from electronic noise for PSA no. 3 and 4. Another feature of the data in fig. 4 follows naturally from eq. (11), i.e., the fact that 6YExp is worst in the middle of the PSA (y or Yo ~ 0) for the roughly segmented anodes no. 1 and 2. Concerning the electronic resolution 6Ynoise, eq. (3) becomes 2

6Ynois e =

62En°ise [1 + (y)2 3,noise( 1 _ (y)2)] 2 ~ (E) • (13)

Using. similar preamplifiers on both sides of the PSA, The rms signal-to-noise ratio ( E ) / 6 E n o i s e depends on the preamplifier used, the cable capacitances Cca b ( ~ 6 0 pF), and the detector capacitances (CpsA in table 1). We measured (E)/ 6 E ~ °lse = ~ E ~ °ise -= 6 E n o i s e.

6Enois e ~ 2 0 0 .

A TSp(t))

o =

Inserting eqs. (A10), (5), (6) and (10) into eq. (3) and identifying (y) = Yo results in

(lO)

We define a noise equivalent capacitance CNEC of our preamplifier (CNEc ~ 270 pF) and a capacitance Co = CNFC + Ccab ~ 330 pF. Then, the noise on one side of the PSA is coupled to the other side according to CpSA/(CpsA + Co). Note that this coupling is anticorrelated. Therefore, eq. (4) may be rewritten ")'noise -

CpSA Cps A + C O

(14)

Since 6Enoise/(E) as well as -Tnoise become larger with an increasing number n of stripes in eq. (13), the resolution 6Ynois e gets worse the finer the segmentation of the PSA. Therefore, it will not be reasonable to choose d very much smaller than the limiting value calculated from eq. (12). Finally, it shou!d be noted that the energy loss signals derived from one side of the PSA become smaller because of coupling to the other side. This changes the sensitivity of the energy loss and, consequently, the position measurement. ( y ) n o longer

565

G. Rosner et al. / A new position measurement

ranges from - 1 to 1, since E R and E L in the generally valid eq. (2) now represent signals derived from the preamplifiers. The coupling factors f = C p s A / C p A are given in table 1. C p A ~ 2 nF denotes the input capacitance of the preamplifiers. The position signal then reads ( y ) ~ (E R) -- (E L) (E R) + (E L)

_ ((1 - f ) ER +f/~L ) -- ((1 --f)LC'L +fgR) ((1 - - f ) E R +J~L ) + ((1 --f)/~L + f e R ) "" (/~R) -- (/~L) ~'~(1 - 2 f ) y o = (1 - zy) (--~R) + (/~.L) '

(15)

where ER, EL denote the energy losses across the PSA. Obviously, (E R) + (E L) = (~'R) + (~L) = (E). Eq. (13) then reads

62Enoise { +( Y0 ~2 ¢32ynoise = 2 ( E ) ~ 1 \ 1 - 2f]

-- 3'noise I1 -- (1Y_~°2f) 21 }.

(16)

The final theoretical position deviation 6YTh (fwhm in ram) for fig. 4 reads 6YTh = 2.35bl(32ynoise + 62ystr) x/2 .

(17)

The agreement with the data is satisfactory. The systematic trends with d and y are reproduced correctly. The resolutions with anodes no. 3 and 4 are limited by the electronic noise. According to eq. (12) the contribution from energy loss straggling is negligible. It becomes important with anodes no. 1 and 2. As expected, anode no. 3 shows the best position resolution. 3.2. Linearity o f the position measurement

n

( r i - li ) g i

n

i=1

_ cos o~ ~ (ri _ l i ) E i . Ed i=1

Y -

(19)

S (r i + l i) Ei i=1 Here, E i denotes the energy loss across the ith stripe, E the total energy loss across the PSA. For 142 MeV 32S, ao = 1.4 °, and anode no. 3, eq. (18) yields a value of k <~ 10 -4 at any point Yo. This is negligible. The experimental nonlinearity ,,y ~Exp in fig. 5, as usual, is determined to be the deviation of the data with respect to a regression line. Though Xy Exp, indeed, is very small for anode no. 3, it is significantly larger than expected from eq. (18). A large systematic dependence of kyZXpony appears for anode no. 1. The reason becomes obvious from the simple model of fig. 6. The shadow with depth d*, which stems from the entrance window and the voltage divider, moves the starting point of the particle track further down the position-sensitive anode. This changes the position information [cf. eq. (1)] in a nonlinear way. Since the nonlinearities caused by the geometry are small, (L~R-- L~L)/(~R + ~L) ~Yo. ~ , L stands for the energy losses across the total right and left parts of the PSA. With the actual energy losses ER, L = L~R,L --E~, L, eq. (1) becomes

(~

- E~)

-

(~

- ED

Y - (~R -- E~) + (L~ - E l ) "

(20)

Assuming the differential energy loss dE/dz to be constant yields ~R + ~L = nd(dE/dz)/cos ot and E~ + E~ = d*(dE/dz)/cos a. A series expansion of eq. (20), and ignoring terms in [(E~ + E~)/(E R + EL) ] 3 results in X = Y - Y o = 1 + ~-~]~--~(Yo -- 1 ) + 2 E L c ° s ~ nd

Though, in principle, systematic nonlinearities of a measurement can be corrected for off-line, it is preferable to have none. Beside tedious computer work, they cause changes in the sensitivity of the experiment. Optimizing the geometry of the positionsensitive anode, we estimated the linearity to be best for the sawtooth configuration of fig. 1. Following the arguments in sections 2.1 and 3.1, and assuming that (dE/dz)i = Ei/d = constant, the geometrical nonlinearity ~. reads (for symbols see fig. 1)

X=y-yo,

with

(18)

(2~) Four cases have to be distinguished, resulting in different values of E~ cos a. Eq. (21) yields X ~< 0 for d* <~d/2 and y>~y* : E~ coso~ = 0

y
•

L7L. C O S O ~ ~

d,_(l+yO)(d

.[.

l+yo]-' Zl ]

.

Further X > 0 for d/2< d*'( d and y >~y* : E [ cos a =½d(1 - Y o )

,

y
(41+ o 1 Z1 !

•

566

G. Rosner et al. / A n e w position measurement

2.0

ii

-2.0

t

f

i i

t

,, L

i J

h i h i

J

t

--

i L

1.0

/

t

~ i

i

/ ,'

i

L i i

,

,

• "*,,,,,,,,,,. ,

®,,..-- t ..x ~

,.<

/

,,A

@

, /;

-

0 UJ:>~

/'

i

i

i

1.o / /

/

i

v

/

/ #i s

/

,

"

.

.4-+

,

~..../..

"i "\',-.-."/i

®

,

/

i

E

v

° R

,

,' ,I

/ ,,

-1.0 _

,,

/

',

Ii

/

,

#

~

i 'w"

-2.0

/

L

f~

(~1

d =60ram

(~ •

d=3Omm

(~)e

d=lOmrn

(~)I

d= 5ram

I -20

I -10

I 0

I 10

I 20

I -20

-1.o

-

-2D

t i i

/

#

-

-30

-

/

I -10

I 0

I 10

I 20

30

y(mm) Fig. 5. Experimental (left) and theoretical (right) nonlinearities Xy for anodes no. l to 4.

Particle ~

~z

/

I

\

Yi" /'

u \

/ /

\ \ \ \

/ \

/ // /

i ii

\

/ // i iI

\ \ \ \

// Target

,Z 1

Eq. (21) has been evaluated with a constant shadow depth of 48 mm for anodes no. 1 to 4. In order to be able to compare the calculated nonlinearity with the experimental one (3`~xp in fig. 5), a regression line has also been fitted to 3`. This has been done within the sensitive width of the PSA. The sensitive region ( - 0 . 6 ~
Fig. 6. Influence of the shadow of the entrance window (hatched area) on the linearity of the position measurement (see text).

567

G. Rosner et al. / A new position measurement

Table 1 Quantities characterizing the position-sensitive anodes (PSA), like the depth d of one stripe, the capacitance CpsA of the PSA, the experimental (Exp) and theoretical (Th) coupling factors f, mean position resolutions 6~ (fwhm) and nonlinearities ~y.

Anode

d (mm)

CpSA (pF)

fExp (%)

fTh (%)

-6YExp (mm)

-6YTh (mm)

~Exp (~am)

~yTh (mm)

1 2 3 4

60 30 10 5

31 34 82 154

1.6 2.7 4.1 7.7

1.6 2.7 4.1 7.7

1.05 0.58 0.33 0.44

0.95 0.62 0.35 0.42

1.23 0.24 0.07 0.03

0.93 0.24 0.17 0.09

of the electrons on the anode, because of the influence of the voltage divider across the entrance window on the path of the electrons. Therefore, the nonlinearities described above, to some extent, will be inevitable. However, the maximum nonlinearities rapidly get smaller with decreasing d, since nd = constant= 120 mm in eq. (21) and d * < d . Consequently, d might be chosen to be smaller in the vicinity of the entrance window. From the partly conflicting tendencies of position resolution and linearity we would estimate anode no. 3 to be the best choice (for our chamber). For this anode, position resolution (fwhm) plus nonlinearity amounts to "q3.4 mm within the full angular acceptance of the chamber.

4. Conclusion It has been shown that the position-sensitive AE anode described in this paper yields precise position measurements with high linearity. The experimental setup is very simple to realize. The influence of energy loss straggling and electronic noise on the position resolution has been described. Therefore, an optimizing prescription could be given. In further experiments, the PSA turned out to work quite well with large area (A~2 = 125 msr) ionization chambers, too [9]. We consider the PSA to be equally adequate for detecting lighter ions in ionization chambers used in magnetic spectrographs.

3.3. Influences on energy, energy loss, and time resolution

Appendix

No negative effects on energy and energy loss resolution were observed by using the position-sensitive anode as first AE anode of the IC. The energy loss resolution is governed by the energy loss straggling across the PSA, which does not depend on the segmentation. Therefore, the additional electronic noise of the PSA, caused by one more PA, plays no role. We measured ~iAE/AE= 3% for elastically scattered 142 MeV 325 ions. The main contributions to the energy resolution are given by the inhomogeneity and energy loss straggling in the entrance foil. The resolution obtained was 5E/E = 0.3%. Since the second coordinate was measured by the IC, the PPAC could be optimized with respect to time resolution. With the setup described in section 2.2 we measured a signal-to-noise ratio of better than 200. The rise time of the signals was less than 2 ns, the time resolution 150 ps.

Here we estimate the resolutions ~Estr,R, ~Estr,L, and the correlation factor 3'str caused by energy loss straggling across the position-sensitive anode (PSA). The main feature of the simple model is the mixing of original energy losses E* or energy loss stragglings ~E*. This is assumed to happen by diffusion as the electrons drift down to the PSA. Thus, the measured energy losses E and their resolution 6E will differ from the original ones. Fig. 7 illustrates this process, o stands for the diffusion width; l and r denote the actual depths of a left and right spike of the PSA. The individual spikes are divided into three parts, depending on whether or not they are affected by the diffusion process. This division is projected onto the particle track. The calculations will be carried out for the right part of the PSA. They are analogous for the left part. Consider, for example, the mixing z o n e ( E L ) i 3 - -

568

G. Rosner et al. / A new position measurement (E~)il (E~)i 2 (E~L)I3 (E~)il .~.,__,~,._A__

(E~)i2 ^

(E~)i3 ,,.._,,_~

Z ~'~ ionization track

\

Frisch grid

segmented anode

~,,...w__> (EL)il

(EL)i2 (EL)J3 (ER)il

(ER)i2

(ER)i3

Fig. 7. Section through the position-sensitive anode along the particle track. Hatched areas denote the diffusion regions (see text).

(ER)il in fig. 7. The measured deviation (~ER)il reads

since 62E[ + 62E~ = 62E * = 62E.

1 * * (6ER)il = (6EL)i3 = ~-[(6EL)i3 + (6ER)il ] .

In order to calculate the correlation coefficient %tr [see eq. (4)], one has to estimate the quantity

(A1)

Assuming the original energy loss stragglings (6E[)q, (~E~)i/, f = 1 , 2 , 3, to be uncorrelated results in 1 ~2(ER)il = ~-[~2(E~)i3 + ~2(E~)il ] .

n

(A2)

3

=

]=1

Since only (6ER)q of neighboring segments are correlated by diffusion [see eq. (A1)], only these terms contribute to the sums in eq. (A8). Applying analogous arguments as in the derivation of ~2Estr,R, we arrive at

It follows from the geometry and 3

= Z) 8 (ED, j=l

[analogously for ~2(/z'~)i] that

o 62(ER)i1 = 4117 62(E[)i + or 62(E~)i] "

(A3)

Analogously 62(ER)i2 -

3

62E

r+l

(A9)

"Ystr - 6E R 6E L

With the actual depth (see fig. 1)

r - 2o r

~2(ER)i3 = ~

(A4)

t~2 (E~)i

~2(E~)i+ 1 + ?

°

~2(E~)

;1

.

(AS)

(A10)

as a function of the geometrical positionyo = y l / b l [-1,1 ], then r + l =d(Yo), r/dO'o)

Finally, n

d(yo) = d(1 +y2o tan2o~o)w2

= (ER)/(E)

= (1 +yo)/2, I/dO'o) = (1 - y o ) / 2 , and eqs. (A6), (A7), (A9) become

3

62Estr,R = ~ ~ 62(ER)i] i:lj=l

~2Fstr,R=(1 +y 0

r - o .o2-* ~ 2 - * , - r - ° r + l (0 /SL + 0 /SR) --~+~/- 62E

O )

2

d(Yo) 82E

(All)

2

d0~o)

(AI2)

(A6) 82E

and l--0 82Estr,L = ~ -

82E,

(A7)

~'str d(Yo) °

1

--~y2o

(A13)

G. Rosner et al. / A new position measurement

References

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569

[5] R. Allemand and G. Thomas, Nucl. Instr. and Meth. 137 (1976) 141. [6] B. Kolb, H. Ingwersen, G. Ihmels, E. Jaeschke, R. Repnow and Th. Walcher, Rev. Phys. Appl. 12 (1977) 1571; B. Kolb, G. Hlawatsch, G. Rosner, Th. Walcher, H. Ingwersen, E. Jaeschke and R. Repnow, Nucl. Instr. and Meth. 188 (1981) 555. [7] H. 'Schmidt-B6cking and K. Hornung, Z. Phys. A286 (1978) 253. [8] E. Mathieson and N. el Hakem, Nucl. Instr. and Meth. 159 (1979) 489. [9] G. Rosner, J. Pochodzalla, B. Heck, G. Hlawatsch, B. Kolb and A. Miczaika, to be published.