Space resolution of drift chambers operated at high gas pressure

NUCLEAR

INSTRUMENTS

AND

METHODS

154 ( 1 9 7 8 )

175-181

; ©

NORTH-HOLLAND

PUBLISHING

CO.

SPACE RESOLUTION OF DRIFT CHAMBERS OPERATED AT HIGH GAS PRESSURE* W. F A R R , J. H E I N T Z E , K. H. H E L L E N B R A N D and A. H. W A L E N T A * *

Physikalisches lnstitut der Universitiit, Heidelberg, Germany Received 27 January 1978 T h e space resolution of a drift c h a m b e r filled with a r g o n / h y d r o c a r b o n mixtures or with hydrocarbons without noble gas a d m i x t u r e was investigated as a function of the gas pressure. It is s h o w n that the space resolution can be substantially improved by rising t h e gas pressure to a few atmospheres. Values of_ 2 5 - 3 5 / a m (rms) at 1-2 c m drift path and of 5 0 / a m (rms) at 5 cm drift path were obtained. T h e results are d i s c u s s e d in t e r m s of the relevant physical processes. Possible applications are briefly considered.

1. Introduction The space resolution of drift chambers operated at atmospheric pressure is mainly limited by two factors: electron diffusion and fluctuations of the primary ionization density. Since bott/ effects are expected to decrease with increasing gas pressure it is interesting to study the space resolution of drift chambers at elevated pressure. Let us consider the effect of the gas pressure p on the electron diffusion. For a single electron drifting during the time t, the rms displacement 6x with respect to the mean driftpath x is =

F

.

D is the diffusion constant, /1 the mobility and E the electrical field. D/U is (up to a constant factor of the order of one) equal to the mean agitation energy of the electrons and depends, therefore, only on the reduced field E/p. At a given value of E/p (i.e. at a given value of the drift velocity % = ttE) 6x is proportional to p ,/2 Since in a drift chamber a swarm of electrons is drifting from the particle track to the anode wire, the diffusion term in the space resolution is smaller than 5x: AXdiff = j B

•x,

B

< 1.

(2)

if the time of arrival of k electrons is recorded by the electronics, n is the number of primary electrons which can compete in arriving first at the anode wire. Although it is difficult to estimate n (and also k) in practical cases, obviously B decreases with increasing ionization density. It is, therefore, expected that Zlxoirf decreases faster than p-,/2 with increasing gas pressure. While the electron diffusion is important for large drift paths, the space resolution for tracks close to the anode wire is limited by fluctuations of the primary ionization density. For tracks with drift path x = 0, this effect contributes to the space resolution a term: 1 Axio, = x/2N, (4) where fi¢ is the average number of primary ionization acts (ionization clusters) per cm (not to be confused with the number of primary ionization electrons per cm). ]V is expected to be proportional

l,O

J E o 20

The factor B which accounts for the statistical effects in the diffusion of a swarm of n electrons can be estimated by the formula'): 1 ,~= l (3) B ~ 21nn = m 2'

IZ

* Work supported by t h e B u n d e s m i n i s t e r i u m ftir F o r s c h u n g u n d Technologic. ** Now at Brookhaven National Laboratory, Upton, N.Y., U.S.A.

Fig. 1. Mean n u m b e r 1 a t m as a function of Experimental data from m e n t s were performed

2k

.I t

01.5

110

I

1.5

of primary ionization acts per cm at t h e gas density p multiplied by Z/A. ref. 2 ( × ) and ref. 3 (e). T h e m e a s u r e with a Sr-90 source (fl.=0.95).

176

w. FARR et

to the electron density of the counting gas and, of course, to p. Experimental values for N are shown in fig. 1. It is seen that AX~on, while being important at atmospheric pressure, can be essentially eliminated by use of dense counting gases at high pressure. Other physical processes which may influence the space resolution of drift chambers are the formation of &-rays and possibly also time fluctuations in the avalanche formation. The pressure dependence of these effects is not obvious. Both will contribute to the space resolution a term which is essentially independent of the drift path. The rms space resolution can then be written: 0 -2 :

A 2 + (AXion) 2 -Jr-(hXdiff) 2 ,

al.

~

ItTtT . . . . . . . . . . . . . . . . IIi I Illil

tTttT1~ . . . . . . . . . . . . . . . . . . III illllJJ

I I il,ol

~l* i idllJ

TTT I ill

~rrTrr ................ Irrrr;r .................. rrr iIIII Ill IJJ

(a)

I

I

II]11

anode

''' '',

I

rrrrTrT. . . . . . . . . . . . . . ; ~ ; r ~ ' ; ~ ~ll~' ~l~' ~ l * l l,ll~ ll t ' J,r~"rgLr-~..,

wires

',l!liliJ

III

lilill

,,............., ........... 2 ,,,, ,,,,

.' r,i

5era i

up

(5)

where the term A, assumed to be independent of x, also accounts for the inaccuracy of the electronic drift time measurement and for the mechanical precision of the chamber. The pressure dependence of the three terms in eq. (5) and their relative importance was investigated experimentally. Not only some commonly used counting gases were studied, but also hydrocarbons with high molecular weight such as propane. In these gases, a low electron energy and a high ionization cluster density can be expected. As shown in the above discussion, this should give rise to a good space resolution. The investigation was motivated by plans to construct a cylindrical drift chamber with high space resolution for the use at e÷e storage rings. A part of the results presented here was already included in the JADE proposal4).

2. Apparatus and measurements The measurements were made using the drift chamber system shown in fig. 2a. A homogeneous drift field was generated by six planes of potential wires and by printed circuit end plates carrying copper strips as indicated by the dashed lines in fig. 2a. The drift spaces were 5 cm long. Three gaps of the system were equiped with anode wires (6 cm long) which were positioned with an accuracy of = 10/~m. The potential wires were carbon coated nylon wires (100 lzm dia.), the anode wires were 2 0 ~ m dia. gold plated tungsten wires. The drift chamber system was placed inside a pressure vessel which also contained three emitter followers connected to the anode wires and a resistor chain connected to the potential wires. The insulation of the chamber was sufficient for drift voltages up to

(b)

Fig. 2. Apparatus: (a) drift chamber, (b) experimental arrangement.

15 kV, i.e. the electrical field in the drift spaces could be brought up to 3 kV/cm. Measurements were carried out at the Bonn Electron Synchrotron. The chamber was placed into a m o m e n t u m analyzed electron beam of l GeV/c beam momentum. The arrangement is shown in fig. 2b. The size of the beam was defined by the 3 x 3 mm 2 lead collimator and by the scintillator hodoscope 123. The beam dimension was 1 m i n x 3 mm at the plane of the drift chamber. The pressure vessel was mounted on a beam scanner and could be moved in the direction transverse to the beam. A simplified block diagram of the electronics is shown in fig. 3. In order to measure the space resScintillator Coincidence

Driftchamber Anode 1

~ =

[ J ~ - - ~ r~. . . . . .

1~

Lo'

r--I

~

Anode 2

Anode 3

DifferenceAmplifier

~ Strobed Coincidence

Fig. 3. Block diagram o f the electronics. D I - D 3 are discriminators, TAC 1, 2 are time to amplitude converters.

SPACE

RESOLUTION

olution of the drift chambers, an analogous signal, proportional to

2(t12t3

~= (tl--t2)--(t2--t3)=

t2) ,

177

CHAMBERS

TABLE 1 Properties of counting gases.

(6)

was fed into a pulse height analyzer, tl, 12, t3 are the drift times measured at the anode wires 1, 2, 3, respectively. A typical C-distribution is shown in fig.4. The rms space resolution of one chamber, a, is related to the.variance of the C-distribution, A~, by the relation: a = ~VD,

OF D R I F T

Gas

Mixing ratio

Ar/CH4

Purity

9:1

Standardcounting gas mixture

2:1 1:2

Ar/Ch4 + iso-CaH]0 C2H4 C3H8 C3H8 +C2H 4

99.95% 99.95% 3:1

(7)

OO being the drift velocity. For a correct measurement of ~, the individual widths and delays of the gate generators shown in fig. 3 must be carefully adjusted., Once this adjustment is done, only the variable "delaying gate" has to be changed in order to compensate the mean drift time x/vD when the chamber is moved to the position x. C-distributions have been measured with the gases and gas mixtures summarized in table 1. In addition, the attempt was made to measure also with propylene C3H6 and with a mixture of 1.8 atm isobutane and 0.8 atm dimethylpropane (a C5H12 clover leaf molecule). These gases showed, however, strong electron attachment. The absence of electron attachment in the gases listed A r / C H t . * C 4 H10(2:1) lotm

•

x = 3.25 cm

" . ~"

•s

i

(o)

: • .

•

•

3. R e s u l t s

The results of the measurements are presented in fig. 6 (a-d). Fig. 6a shows the rms space resolutions cr as a function of the drift path x for

"."i •

•

" °%

in table 1 was controlled by measuring the pulse height as a function of the drift path x. Up to x = 5 cm and within a precision of 59(, no drop of pulse height was observed. W h e n varying the pressure, the drift voltages were changed in order to keep the reduced field strengths E/p at constant values. Fig. 5 shows the drift velocities for the gases used here as a function of E/p. The anode voltages were adjusted so that the most probable pulse height for m i n i m u m ionizing particles was Um= 10--20 mV at the emitter follower (1 kI2 input impedance, --~5 ns rise time). The thresholds of the discriminators D~, D2 and D3 (fig. 3) were adjusted to values corresponding to 0.5 mV at the emitter follower.

0 2 4 6ns °

t,l.|,l

I

6

%

;. •

¢;

,..,~.,,..',.v.2:~.'.'~.\"

""2~..,,~,.~ . ~

2 I

C3H 8 ÷ C2Ht,(3:1) 4 atm

x = tcm

(b)

I

I

I

I

Ar/CHI. I

I

I

I

I

I

I

I

/

:~.. "*

0 2 t. 6ns t,l,l,I

l/

I

0.~

0.8

1.2

E (

kV

~._~

p ~ cm atrn t

Fig. 4. Distributions of the quantity ~j defined by eq. (6); (a) corresponds to arms space resolution of a = 140 #m, (b) corresponds to cr= 26 #m.

Fig. 5. Drift velocity o19 as a function of the reduced field strength E/p. Measurements of the space resolution were made at the points indicated on the curves.

178

w.

FARR et al.

~AF/CH4.½C4 H10 ---x-C3 H8 Ar/CHt, - - o - - / . ~ 3 otto 15

/~s/~,.I otrn

100

' ~ S l/ISleS •

s/

3atm

"="= s S ' d - ~ = ~ 3....o- ot rn ,.,,jis:.~

j

~

Zatm

/- -

/

t, atm 6atm

(a) i

i

i

I

I

C2 H4

I

I

I

I

3 C 3 H8+ / C 2 Hi. / . T , , - I atm

100

50

(b) I

~

~

......a- 3 at m

(c) t

a

J

I

I

(d) I

I

I

/

I

2 4 2 4 x(cm) --~ Fig. 6. Root mean square space resolution a as a function of the drift path x.

argon/methane and argon/isobutane mixtures. Fig. 6b shows results for propane which was investigated for the reasons outlined in section 1. Fig. 6c shows results for ethylene. Although this gas is not as good a counting gas as other hydrocarbons, it was examined because it is known to have a low diffusion coefficient. The best results !1~

150

Discriminatorthreshold

(a) 100 50

O(lam), 40

were obtained with a mixture of propane and ethylene (fig. 6d). At a pressure of 4 atm the space resolution obtained with this gas was better than 50/~m at a drift path of 5 cm. The dependence of the space resolution from the most probable pulse height u m was investigated with ethylene. The results (fig. 7a) demonstrate that in the "range um= 10-20 mV, where the results presented in fig. 6 were obtained, the space resolution has already reached a saturation value. The space resolution measured with Um~ u = 0.5 mV is tr = 160/.tm, corresponding to expectation: The half width of the time spectrum is 2.36× 160 #m/4.5 cm/,zs -l = 8.5 ns. This is approximately equal to the rise time of the anode signal at the discriminator input. The space resolution was also measured as a function of the beam momentum. The results (fig. 7b) show, that multiple scattering of the beam did not contribute significantly to the measured space resolution. 4. Discussion

The qualitative features of the curves shown in fig. 6 correspond to expectation. The cluster effect producing the sharp increase of tr close to the anode wire and the diffusion effect producing the slow increase of cr for large x are clearly visible. The influence of both effects diminishes with increasing gas pressure. The data obtained at atmospheric pressure (fig. 6a) are in agreement with previously reported results on the space resolution in similar counting gas mixturesS.6). It should be noted, however, that also better values for the space resolution at atmospheric pressure have been reported 15). In fig. 8 (a-f) the mean square space resolution. a 2 is plotted as a function of the drift path x. Straight lines are fitted by eye through the points x ~>1 cm. These lines should be represented by the equation (cf. section 1): o ~

2BD

= A s + --~-- x.

(8)

(b)

20

Fig. 7. Space resolution as a function of the most probable pulse height for m i n i m u m ionizing particles (a) and o f the beam m o m e n t u m (b).

The values for BD/IJ which correspond to the slopes of the fitted lines are plotted in fig. 9 as a function of the pressure. Since D/la - for constant E / p - should be independent of the pressure, the observed decrease of BD/IJ with rising pressure is attributed to a decrease of B. Such a decrease is expected (section 1). The data presented in fig. 9 may be compared with experimental values of D/la. From diffusion

SPACE

Ar/ _

%

C/

RESOLUTION

~I

2.C

(10-2v)

~Ar/CHt,*~Ct,HI0/

o

1.0

1.C u•

0.5 I

I

I

I

I

0.5 (al

%,

1.5 10

~

I

3

I

~

I

I

1.0

(b)

I

3 otto

I

I

I

I

I

I

1 otrn

2 ottoI0

/ 7 / ,

|

I

I

I

,~

p (otm)---~ Fig. 9. "Effective electron energy" BD/p as a function of the gas pressure.

I ÷J4~ 1

.- ~3 c 3 1 - ~1 ~ ,

C3 H8 1.0

I

I

2

(d) I

x

aim

05 I

ClAr/CHt. x ~Ar/CH4 ÷~Ct.Ht0 ÷ ffAr/CHt, * ~3Ct,H10 0 C3H8 e~C3H8- ¼C2H& • C2H4

13

2.0

1.c.

1.5

179

CHAMBERS

BQ

otto

~ 3 air

OF D R I F T

atrn0'5

l,~/==a~6

atm i i i I (el i t t (f) 2 Z, 2 t, x ( c m ) ~ Fig. 8. Mean square space resolution a 2 as a function of the drift path x. The straight lines are fitted by eye to the data points x>~ 1 cm [cf. eq. (8)].

measurements in Ar/CH4 mixtures7), we deduce D / / ~ = 0 . 2 4 V at E/p=O.33kV/cm atm for an Ar/CH4 mixture with 10% CH4. In ethylene, D//~=0.08 V was measured at E/p=0.66 kV/ cm atm 8). These values, which have been determined by measurements of the diffusion transverse to the drift direction, are about a factor l0 higher than the corresponding BD/p values in fig. 9. Since this factor may be partially due to a difference in diffusion transverse and parallel to the drift directiong), it is not possible to derive the magnitude of B from this comparison. With reference to eq. (1), the quantity BD/p may be defined as the "effective electron energy". It is remarkably lower than the true mean agitation energy of the drifting electrons.

From fig. 8 and eq. (8) also the drift path independent term A can be derived. Results are compiled in table 2. There is no apparent pressure dependence of A. The term A seems to depend, however, on the composition of the counting gas. The latter observation suggests that 6-rays give not the main contribution to the term A. Both the range and the production probability of 6-rays depend in first approximation only on the gas density and not on the atomic composition of the gas. Furthermore, 6-rays should give rise to pronounced non-Gaussian tails in the C-distribution which were not observed in this experiment (fig. 4b). We can also perform a quantitative estimate of the 6-ray contribution. The "true range", i.e. the mean path length of low energy electrons in gases has been determined in cloud chambers 1°) and, indirectly, by ionization measurementstl). Because of the extremely strong scattering of low energy electrons, this quantity is not useful for our estimate. We should rather call in data on the absorption of electrons at diffuse incidence. Such data are available from the early work on cathode rayst2). It was found that the absorption of low energy electrons is approximately exponential. The adequate quantity for our estimate is, therefore,

TABLE 2

Drift path independent contribution to the space resolution. Gas

A (p m)

Ar/CH 4

55

A r / C H 4 + i C4Hl0 2:1 1:2

55

42

C2H 4

C3H 8

C2H 4 + C a l l 8 3:1

35

25

20

180

w. FARR et

the "absorption length" i.e. the reciprocal of the absorption coefficient. In fig. 10, the absorption length 2 and, for comparison, also the range of low energy electrons is plotted. The probability that a minimum ionizing particle produces a 6-ray with an energy bigger than a certain value T in 1 cm of gas with the density p

al.

I000

°'r t 02 Ar air

isl3):

0.075 p(mg/cm 3) W(T) ,~ T (keV)

( Ref. 10)

x =

(Ref, 11) Xo

100

,x x

(9)

Since the absorption length is roughly proportional to T 2/p, the probability to produce a 6-ray with an absorption length bigger than a certain value 2 is roughly proportional to (p/2) 1/2. In a gas with p = 2 m g / c m 3, a 6-ray with 2 = 10 a m has an energy T = 3 keV. The probability to produce in 1 cm of the gas a f-ray with T > 3 keV is only 596. We conclude that 6-rays are not expected to give a major contribution to the A-values reported in table 2. Tentatively, the observed effects may be attributed to time fluctuations in the avalanche formation process. A quantitative analysis of the term AXio, [eq. (4)] is not possible in this experiment since the width of the beam was about 1 ram. The qualitative observation is that the space resolution for tracks close to the anode wire becomes better with rising ionization cluster density N as expected. 5. Conclusions

By application of high pressure (a few atmospheres) the-space resolution of drift chambers can be substantially improved. The observed behaviour of the space resolution is essentially understood. The most important effect in chambers with long drift paths is a strong suppression of the electron diffusion: At high pressure drift spaces of 10 cm can be used while maintaining a space resolution a < 1 0 0 a m . For drift chambers with short drift paths (up to 2 cm) the" space resolution is dominated by a term which is independent of the length of the drift path. In this case the use of propane or propane/ethylene mixtures is especially favourable. Space resolutions of ~ 30 a m can be obtained. The technique proposed here which requires a pressure vessel is suitable for cylindrical drift chambers surrounding the interaction point of a storage ring or surrounding a target. A large chamber of this type which is to be used in the JADE experiment 4) at PETRA is presently under

•x

=L

x

(a)

•

10

(b)

g

• tlir 1 x

0.1

S

0.1

CO2

Ref.

12

Ar j

I

10

Electron energy Ike71 Fig. 10. Range of low energy electrons; (a) mean path lengths. The curve represents the results of a recent calculationl4); (b) absorption length. The curve is a fit to the data proposed by P. Lenard 12).

construction at our laboratory. The technique may also be useful for the construction of vertex chambers for studying the decay of particles in flight or for small beam chambers if a very good space resolution is important. We greatly acknowledge the generous support which we have received at the Bonn Electron Synchrotron by our colleagues. In particular Dr. Husmann contributed very substantially to this work by his advice regarding the beam and by supplying equipment. For the construction of the chamber we thank Mr. Ehrbar and the mechanical workshop of our institute as well as Mr. Bruder and Mr. Witzmann who supplied the very precise wire suspensions. References 1) H. Cram6r, Mathematical methods o f statistics (Princeton University Press, 1966) p. 374. 2) A. H. Walenta, Lokalisierung yon Teilchenspuren durch Messung der Elektronendr(ftzeit in groflfl?ichigen Proportionalziihlern, Dissertation Heidelberg (1972); the value/V shown in fig. 1 was obtained by measuring the inefficiency of a thin drift chamber.

SPACE RESOLUTION OF DRIFT CHAMBERS 3) K. O. Greulich, Einfiufl yon Ziihlgasgemischen auf Driftzeitkurven und Dr~l'tzeitverteilungen in einer Vieldraht-Dr(/?kammer, Diplomarbeit Heidelberg (1973); the results shown in fig. 1 were obtained by measuring the drift time distribution from particles injected at the anode wire. 4) " A proposal for a compact magnetic detector at PETRA (JADE)", Daresbury-DESY-Hamburg-Heidelberg-Lancaster-Manchester-Tokyo. Spokesman R. Felst, DESY. Proposal PETRA 76/16 (August 1976). 5) j. Heintze and A. H. Walenta, Nucl. Instr. and Meth. 111 (1973) 461. 6) A. Berskin, G. Charpak, F. Sauli, M. Atkinson and G. Schultz, Nucl. Instr. and Meth. 124 (1975) 189. 7) D. R. Nygren, Proc. of the 1975 PEP Summer Study, LBL4800/SLAC-190/PEP 178, p. I26. 8) L. W. Cochran and D. W. Forester, Phys. Rev. 126 (1962) 1785.

181

9) j. H. Parker and J. J. Lowke, Phys. Rev. 181 (1969) 290, 302. 10) O. Klempe~'er, Einfiihrung in die Elektronik (Berlin, 1933) p. 272. It) E. Buchmann, Ann. d. Phys. 87 (1928) 509. 12) p. Lenard, Ann. d. Phys. 12 (1903) 714; Wied. Ann. 56 (1895) 255; See also: W. Bothe, Durchgang yon Elektronen durch Materie, Handbuch der Physik XXII/2 (Springer-Verlag, Heidelberg, 1933). 13) B. Rossi, High energy particles (Prentice-Hall Inc., Englewood Cliffs, N.J. 1952) p. 17. 14) L. Pages, E. Bertel, H. Joffre and L. Sklavenitis, Atomic Data 4 (1972) 1. 15) N. A. Filatova, T. S- Nigmanov, V. P. Pugachevich, V. D. Riabtsov, M. D. Shafranov, E. N. Tsyganov, D. V. Uralsky, A. S. Vodopianov, F. Sauli and M. Atac, Nucl. Instr. and Meth. 143 (1977) 17.