Guidelines for a supercollider experiment: the magnetic system

Nuclear Instruments and Methods in Physics Research A307 (1991) 247-253 North-Holland

247

Guidelines for a supercollider experiment: the magnetic system P. Spillantini a a n d Y.F. W a n g 1 INFN Sezione di Firenze, Florence, Italy Received 13 September 1990 and in revised form 8 April 1991

We try to give some general guidelines for optimizing the magnetic system of a general-purpose detector with a high momentum resolution for muons at a supercollider experiment. Solenoidal and toroidal schemes are investigated, with the possibility of using calorimeter material as the coil.

1. Introduction With the highest luminosity of the proposed Large Hadron Coilider (LHC) and Superconducting Super Collider (SSC), the muon channels will be the most clear, if not the only ones, that can be studied. There are proposals for experiments which suggest to measure to m u o n m o m e n t u m with extremely high precision, say a few percent in the m o m e n t u m range of 0.1-1 TeV, to reconstruct parent masses precisely a n d / o r to have a signal not to be flood by backgrounds [1]. The classical way of measuring the Ix momentum, by its bending in the iron used to return the field of the central spectrometer, gives a precision on the momentum of not better than ( 0 . 4 1 / B ) / v ~ ( L is the length of the path in the spectrometer, normally a few meters; B is the magnetic field in the iron, normally less than 2 T), because of the multiple scattering in the iron, independent of the value of the momentum. One way to reduce the effect of multiple scattering is to let the ix be bent in free space in a magnetic field B and on a sufficiently long path L: the magnet used to produce B must enclose the IX spectrometer and cover a wide solid angle. This means that the geometrical dimension of the magnet tend to be enormous and also, if L is more effective than B to minimize the measurement error, that a compromise with B must be obtained, since the I~ m o m e n t u m resolution has a ( B L 2)- 1 dependence.

2. A solenoid-based experiment When we assume the straightforward solution of a solenoidal magnet with a warm coil, there exists an 1 Visitor at CERN, Geneva, Switzerland.

optimal path length Lop t which, for a given electric power P supplied to the magnet coil, minimizes the weight of the magnetic system (coil + iron yoke to close the magnetic circuit). Naturally, in the final project of an experiment based on such a magnet, Lop t must be balanced with the cost and complexity of the IX detector, with the dimensions of the experimental hall, etc. This kind of optimization should be done seperately for the barrel and the end-cap part of the detector. In this article we only present an analysis for the barrel part, which corresponds to a coverage of 1711 < 1. To give a definite basis to our reasoning we assume a solenoidal aluminium coil enclosed in an iron yoke that returns the magnetic field (iron barrel) and makes it uniform inside the coil (iron end caps). For quantitative evaluations, a set of hypotheses must be assumed: (a) on the coil itself (Aft covered, space in the coil for cooling), and (b) on the IX detector (distances of its useful volume from the coil, alignment, multiple scattering and measurement precisions, minim u m radius of its useful volume). However, the hypotheses on the rest of the detectors (i.e. the calorimeters to filter the muons and the vertex detectors) are irrelevant to the argument. We derive the values for both (a) and (b) from the case of the L3 experiment [2] at the Large E l e c t r o n Positron storage ring (LEP), which is an example of a setup best suiting our problem: (a.1) The conductor is aluminium and the magneticfield induction in the iron is assumed to be 1.8T. (a.2) Because of cooling and the structure of the supporting system, the radial thickness A R of the coil is twice the conductor thickness (t = ~ AR, ~ = 0.5). (a.3) The length L~ of the IX detector is twice its external radius R e in order tO cover zenith angles from 45 ° to 135 °

0168-9002/91/$03.50 © 1991 - Elsevier Science Publishers B.V. All rights reserved

P. SpillantinL Y.F Wang / Supercolliderexperiment

248

0.5 m

R

Re] ~

/

Lit

J,l

,~

j

Lb Magnet free-bore

0.3 rn ,

,

10m

i

t. . . . r _ _ L _ _ 4 . . . . . . . . . . . . . . . . . . . . . . . . . . l 7--Calorimeter (outer section)

_+. . . . . . . . . . . .

i ~

~t-detec{or useful volume

Fig. 1. Assumptions for the ~t detector.

(b.1) The last p o i n t in the ~ trajectory is m e a s u r e d at a radius R e, 0.5 m smaller than the radius R of the useful magnetic field volume, R e = R - 0.5 m. A l o n g the b e a m axis the ~t detector is supposed to b e efficient over a length L~, 0.8 m shorter t h a n the length L b of the useful magnetic v o l u m e , L~ = L b - 0.8 m. These are the a s s u m p t i o n s illustrated in fig. 1. (b.2) The first p o i n t in the ~t trajectory is m e a s u r e d at a distance R i = 3.0 m from the b e a m axis ( c o m p a r e d with R i = 2.52 m for L3). T h e systematic error o n the sagitta S is assumed to be 30 rtm, multiple scattering error 3.8 ~ m at p = 500 GeV, a n d the ~t is supposed to

60

Fe

,~ . k.. /-,it-\

. . . . AI coil

\

.__

/ /

l y

50--

-~ 40 -

Ri)2B/p],

(1)

P = PA,21r(Re + 0.5 +

_

where PAl is the conductivity of aluminium. G i v e n the sagitta S a n d the total electric power P, the thickness (t = 71 A R ) of the solenoid can b e deduced as a f u n c t i o n of the external radius R e of the # detector. The thickness of the coil determines the outer d i m e n s i o n a n d the weight of the coil, a n d defines the magnetic-field volume. The cross section, a n d t h e n the weight of the iron yoke, which is needed to r e t u r n the m a g n e t i c field inside the solenoid, is d e t e r m i n e d from a simple relation:

-

\~

t)I2/(L~t).

1

-

30

(2)

Magnetic flux ( B = 1.8 T ) in the iron = Magnetic flux in the solenoid,

20-

10

S = (0.3//8) [ ( R e -

where B = #o I/Lb (I is the total current). T h e electric power P can be expressed as a f u n c t i o n of the electric current:

S/S500 =1 70--

b e measured in a set of detectors with a precision of 150 ~tm per point, giving a global m e a s u r e m e n t precision of 48 ~tm at p = 500 GeV. In order to measure the d i m u o n mass with a precision of 1.29% at 1 TeV ( t h a t is the precision o b t a i n e d by L3 for a d i m u o n mass of 100 GeV), the c o r r e s p o n d i n g sagitta is $500 = 2.62 m m (the index 500 indicates the m o m e n t u m in G e V of one of the two m u o n s in a symmetric d i m u o n of 1 TeV). F r o m the classical electromagnatic field theory, one can relate the sagitta S to the m a g n e t i c field B:

-

.25

"---[-2zzz==========3?===--0 --

10 Re

(m)

20

Fig. 2. Solenoid: weight of the AI (broken lines) and of the Fe (full lines) coil for different values of the sagitta S.

using the above inputs. The results, parametrizing the ratio between the sagitta S a n d the reference value $500 = 2.62 ram, are reported in fig. 2, evaluated for a n electric power P = 12 M W spent o n the coil. As s h o w n in fig. 2, for each o b t a i n a b l e precision in the m o m e n t u m m e a s u r e m e n t (expressed by the S/$5o o parameter), there exists a n optimal external radius -Re°pt Of the rt detector for which the total weight of the iron is a m i n i m u m . The weight of

P. Spillantini, Y.F. Wang / Supercollider experiment the aluminium coil is one order of magnitude lower, and decreases monotonically with R eThe weight of these two components is related to the total price of the magnet. However, the prices of the raw materials are substantially different and constitute only a fraction of the total cost, which should include also the cost of the manufacturing, the necessary equipments, the assembling, the installation and the supporting structure. In particular the complexity and the cost of the installation and the supporting structure could depend more than linearly on the total weight. Also for this reason we believe that the weight of the iron, which is more than 90% of the total weight, could be considered as a significant guiding parameter for the total cost. In the whole energy range the values of the current density in the aluminium coil are very low, i.e. between 0.4 and 1.5 A / m m 2, so that the cross section foreseen for the cooling in the above hypotheses (a.2) is more than sufficient. The values of the magnetic field range from 0.1 to 0.7 T. The minimum iron weight deduced from fig. 2 strongly depends (nearly linearly) on the obtainable precision. Allowing a 10% (20%) increase of the iron weight the optimal external radius R e°pt diminishes more than 20% (25%), as shown in fig. 3; this is an important point for calculating the dimensions of an experimental project,

I

I

I

20 -

.-'"""

50

249

I

I

\

I

./ .

I

......

30 - """ . . . . . . . . . J l " ~ x ' x Fe x:: ._~

20 -

10 " 0 R

~ i=3.5m ' R /AIc°il i 10

'

~

..... 15

Re(m)

I ..... 20

I 25

Fig. 4. Solenoid: weight variation for different minimum radii of the I~ detector. weighing the magnet price against the I~ detector price and complexity. The dependence of the weight of the coil and of the iron yoke on R e for S = Ss0o is reported in fig. 4, allowing the inner radius R i to vary by _+0.5 m around the 3.0 m value assumed in the above evaluations. It results that the weight and R e°pt variations with R i a r e of secondary importance: A drastic reduction of the " v e r t e x + calorimeter" external radius from 2.7 m (corresponding t o R i = 3 . 0 m ) t o 2.2 m (corresponding to R i = 2 . 5 m ) results in an 11% reduction in the iron weight and less than 7% in R °pt.

...--'"

"'"""

9

S

rr ~

e

~

..........~22-2-

1o

I 0

0.5

I 1.0 s/s 500

t 1.5

Fig. 3. External radius of the tt detector for " minimum", "minimum+10%" and "minimum+20%" iron weight, as a fuction of the sagitta S. The variation of the iron weight has been taken at both left and right sides of the minimum reported in fig. 2,

3. P o s s i b l e u s e o f t h e c a l o r i m e t e r m a t e r i a l f o r t h e m a g netic system

In the solenoid case discussed above, the elements of the magnet (coil + iron yoke) are not used as part of the detectors, unlike what happens in the "classical scheme" where the absorbing material of the calorimeter (normally iron) is used to return the magnetic flux. Could this absorbing material be used in a different way, e.g. for carrying electric current to produce a magnetic field in the volume of the I~ detector? Obviously the iron of the "classical scheme" should be replace by copper, suitable to conduct electric current and also better than the iron as an absorber in a calorimeter. Two schemes can be foreseen: The current would flow in circles around the beam axis, producing a solenoidal field that starts inside the calorimeter and closes outside, mainly in the ~ detector volume (fig. 5);

250

P. Spillantini, Y.F. Wang / Supercollider experiment 3.1. Possible use of the calorimeter material for the solenoidal system

Electric current in the coil

~

Bin

Fig. 5. The "partially compensated" solenoidal scheme.

or the current would flow parallel to the beam axis, producing a magnetic field only outside the calorimeter, whose lines are circles centered on the beam axis (toroidal field, see fig. 6). In the following two sections these two possible scenarios will be discussed, assuming for the calorimeter design the following set of hypothesis. Only the absorbing material of the external part of the calorimeter, the so-called "tail catcher", will carry the electric current; this part is assumed to extend from 2.7 m down to 1.4 m distance from the beam axis and to have a 10 m length in order to cover up to 30 ° in zenith: This is the calorimeter (outer section) shown in fig. 1. The detector is assumed to occupy a quarter of the corresponding cross section, while the cross section devoted to the cooling is assumed to be negligible, provided that the electric current density is kept to less than 2 A / m m 2. The ratio between the copper cross section and the total geometrical cross section is indeed ~¢ = 0.75. The innermost part of the calorimeter is not involved in order to preserve the complete freedom of using the best materials and techniques to optimize the energy resolution. The power spent in the whole magnetic system will still be assumed to be P = 12 MW.

The coil and iron weights are calculated now solving the above relations for the whole magnetic system (solenoidal coil + calorimeter + iron yoke), allowing the current density in the calorimeter to vary from 0 to 2 A / m m 2 in the copper. The results (fig. 7) are not much different from the previous ones reported in fig. 2. Two important remarks must be made concerning this scheme. Firstly, the use of the outer part of the calorimeter as a solenoid, even if it does not help in the magnetic system for the ~ spectrometer, can produce a very high field in the interaction region, from which a vertex detector could largely profit. Secondly, given the smaller dimensions of the calorimeter compared with those of the p. spectrometer, the " v e r t e x + calorimeter" part could be enclosed in a superconducting coil, which, besides contributing to the field in the ~t detector, would assure a high field in the vertex region; obviously its radial dimension should be considered in the optimization of the whole system. 3.2. Possible use of the calorimeter material for the toroidal system To compare this second scheme with the previous ones, the geometry of the rt detector must be redrawn (fig. 8) in order to match the different trends of the m o m e n t u m resolution in the toroidal field (see fig. 9). The magnetic system consists now of the outer part of the calorimeter and of a conductor that closes the current circuit and also defines the magnetic-field

B in (Tesla) 501

1

2

3

4

5

6

7

i

i

i

i

r

i

i

8 i

~" 40

=

2

jJl~

f/ ~,~ ;" f J ~ . ~ - )

j~-"

~

~-r I ~

~ .--7 Electric current

~-J

~

/~loop closed outside ~" in cylindrical "~-' symmetry

~.f J~

in the calorimeter

Fig. 6. The toroidal scheme.

~

E

~ E 3o

20 °'.2 01, °'.8 018 110

115

210

kin (Nmm 2)

Fig. 7. The mimmum iron weight as a function of current, using the calorimeter material for the solenoidal system.

251

P. Spillantini, Y.F. Wang /Supercolfiderexperiment

60 ~ 0.5~m

/ J

'~

~

. 0.4 m--~ ~ Ri

Calodmeter~nJCu)" 1.6Re

45~

L,,/ -~,l ir~---0.4 m

Fig. 8. Assumptions for the I• detector using the calorimeter material in the toroidal system.

volume where the ~t detector operates (see fig. 8). N o iron is present to r e t u r n the field, as it closes on itself in circular lines. Its s t r e n g t h diminishes as 1 / R with the distance R from the b e a m axis, a n d eq. (1) for the sagitta modifies to

S = [O.O15IRi(Y- 1 - In y ) ] / p

( y = R e / R i ) . (3)

In order to have the field d e p e n d i n g as m u c h as possible only o n R, the shape of the c o n d u c t o r closing the c u r r e n t circuit should approach, as m u c h as possible, t h a t of a cylinder. A n i m p o r t a n t p a r a m e t e r d e t e r m i n i n g the strength of the field a n d the electric c o n s u m p t i o n is the ratio rs of the total cross section of this c o n d u c t o r to the cross section of the c o n d u c t o r in the calorimeter.

15

Toroid "equiresol 10 E Cc

15

Ri=

z(m)

20

10

Fig. 9. Toroidal field map in the I~ detector using the calorimeter material.

P. Spillantini, Y.F Wang / Supercollider experiment

252

1.50

9~

1.75

8

o7 ~:

5

"6 4

2 1 I

I

I

[

I

I

5

10

15

20

25

30

R e (m) Fig. 10. The weight of the AI conductor as a function of external radius of the ~t detector.

A s s u m i n g t h a t t h i s c o n d u c t o r will b e m a d e o f a l u m i n i u m , t h e a b o v e eq. (2) a n d (3) s o l v e d for its t h i c k n e s s give t h e w e i g h t s r e p o r t e d in fig. 10 as a f u n c t i o n o f R e, t h e p a r a m e t e r r s a n d t h e o b t a i n a b l e m o m e n t u m r e s o l u t i o n e x p r e s s e d as S / $ 5 o o.

I

I

I

-~

20

/ ,oy/

T h e R e v a l u e s for r s = 2 a n d 3 a r e c o m p a r e d in fig. 11 w i t h t h o s e o f t h e " m i n i m u m i r o n w e i g h t " a l u m i n i u m s o l e n o i d o f fig. 3, as a f u n c t i o n o f S / $ 5 o o. F o r S / $ 5 o o < 1 t h e radial d i m e n s i o n s o f t h e ~ d e t e c t o r in this t o r o i d a l s c h e m e a r e s i g n i f i c a n t l y s m a l l e r t h a n t h o s e in t h e s o l e n o i d a l o n e ; this a d v a n t a g e a d d s to t h e s h o r t e r L b r e q u i r e d b y t h e t o r o i d a l s c h e m e . It m u s t b e n o t e d t h a t for i n c r e a s i n g rs t h e t o t a l electric r e s i s t a n c e o f t h e coil d e c r e a s e s , a l l o w i n g R e to d e c r e a s e ; h o w e v e r , this t r e n d is effective u p to r~ = 3 - 3 . 5 , a n d d e c r e a s e s a f t e r w a r d s at t h e e x p e n s e s o f a s h a r p i n c r e a s e in t h e c o n d u c t o r w e i g h t . It m u s t f i n a l l y b e n o t e d t h a t in t h e c a s e o f t h e s o l e n o i d a n e x t r a w e i g h t m u s t b e c o n s i d e r e d for t h e s t r u c t u r e s u p p o r t i n g t h e c a l o r i m e t e r at t h e c e n t e r o f t h e ~t d e t e c t o r ; in t h e c a s e o f t h e t o r o i d a l s c h e m e a s u i t a b l e d e s i g n c o u l d e n a b l e t h e a l u m i n i u m c o n d u c t o r to b e

v

Table 1 Comparison of dimensions and weights for different magnetic configurations

10

Magnet

I

0

0.5

E

1.0 S/S 500

I

1.5

Fig. 11. The external radius of the ~ detection volume as a function of sagitta for different values of r s.

Re [m]

L, [m]

Material

Weight [t]

Toroid rs = 1 rs = 2 rs = 2 rs = 3 rs = 3

15.2 14.3 12.5 12.8 11.5

24.3 23.9 20.0 20.5 18.4

Cu AI Cu Al Cu

5876 3331 9536 4447 13 119

Solenoid

13.4

26.8

AI + Fe

2542 33 275

F

SpillantinL T.F Wang / Supercollider experiment

20

20

253

self-supporting, a n d p e r h a p s to s u p p o r t the calorimeter as well. A substantial reduction of the d i m e n s i o n s of the F detector, at the price of a large increase in weight of the current c o n d u c t o r can b e achieved b y using c o p p e r for this conductor, given its b e t t e r conductivity. T h e final c o m p a r i s o n for S/$5o o = 1 is s h o w n in table 1. Finally, fig. 12 shows h o w the d i m e n s i o n s of the detector a n d the weight of the a l u m i n i u m c o n d u c t o r vary with the a b s o r b e d electric power.

°-10

References

o 10

I 15

t 20 R e (m)

I

0

25

Fig. 12. The F detector dimensions as a function of the weight of the AI conductor for different values of electric power.

[1] U. Becker, et al., Workshop on Experiments, Detectors and Experimental Areas for the Supercollider, Berkeley, July 1987 (World Scientific, 1988), p. 525; P. Duinker and K. Eggert, Large Hadron Collider Workshop, Aachen, October 1990, CERN 90-10, vol. I, p. 452; L* Collaboration, Letter of Intent to the SSC Laboratory (November 1990). [2] B. Adeva et al. (L3 Collaboration), Nucl. Instr. and Meth. A289 (1990) 35.