cern/si/int. dl/70-10 basic explllissions poh evaluating...
TRANSCRIPT
![Page 1: CERN/SI/Int. DL/70-10 BASIC EXPllliSSIONS POH EVALUATING ...cds.cern.ch/record/1462804/files/CERN-SI-INT-DL70-10.pdf · cern/si/int. dl/70-10 7.12.1970 basic explllissions poh evaluating](https://reader033.vdocument.in/reader033/viewer/2022060313/5f0b6a5b7e708231d4306866/html5/thumbnails/1.jpg)
CERN/SI/Int. DL/70-10 7.12.1970
BASIC EXPllliSSIONS POH EVALUATING IRON CORE MAGNETS
A POSSIBLE PROCEDURE TO MINIMIZE THEIR COST
G. Brianti and M. Gabriel
l. Description of the magnet 1.1 Dimensions and geometrical parameters 1.2 Other parameters
2. Active power
3. Volume of conductor
4. Volume of yoke 4.1 Volume of yoke for magnets with two return yokes 4.2 Volume of yoke for C magnet with pole 4.3 Volume of yoke for C magnet of window-frame type
5. Stored energy 5.1 Stored energy for magnets with two return yokes 5.2 Stored energy for magnets with one return yoke
5.2 a) Window-frame type 5.2 b) Pole type
6. Possible values for the coefficients c 1 and Ki
7, A possible optimization procedure 7.1 M - cost of power supply and associated equipment 7.2 M
1 -cost of finished coil
7.3 M~- cost of finished yoke 7,4 M
4- cost of a.c. and d.c. power distribution
7.5 M5
- cost of cooling 7.6 M cost of electricity 7.7 cSst normalization 7.8 Example of application
7.8.1 Cost coefficients ?.8.2 Results of computations and a possible choice
8. Conclusions
Acknowledgements
References
![Page 2: CERN/SI/Int. DL/70-10 BASIC EXPllliSSIONS POH EVALUATING ...cds.cern.ch/record/1462804/files/CERN-SI-INT-DL70-10.pdf · cern/si/int. dl/70-10 7.12.1970 basic explllissions poh evaluating](https://reader033.vdocument.in/reader033/viewer/2022060313/5f0b6a5b7e708231d4306866/html5/thumbnails/2.jpg)
![Page 3: CERN/SI/Int. DL/70-10 BASIC EXPllliSSIONS POH EVALUATING ...cds.cern.ch/record/1462804/files/CERN-SI-INT-DL70-10.pdf · cern/si/int. dl/70-10 7.12.1970 basic explllissions poh evaluating](https://reader033.vdocument.in/reader033/viewer/2022060313/5f0b6a5b7e708231d4306866/html5/thumbnails/3.jpg)
-
- l -
It is often useful to estimate the power and the volume
of a magnet prior to its actual detailed design. Expressions
for these quantities as function of the characteristics of the
beam and of the minimum possible number of magnet parameters may be
helpful both for :
a) evaluating the implications and the cost of a beam;
b) directing the actual magnet design to minimize the
investment cost or the investment plus running cost for
a given time.
In what follows, these expressions are given together with
an actual example. A possible procedure for minimizing the overall
cost is indicated, it makes use of both the magnetic length L
(or gap field B) and the current density j as main parameters.
1. Description of the magnet
A magnet giving a uniform field in the be= reg~o::c. is
assumed throughout the report (bending magnec). All the types
of magnet most commonly used are considered, as sho·.m in Fig. :, c..
and b), and expressions for both d.c. a.'ld pulsed :na.gnets are given.
It will be seen that, in most cases, it is possible to wori:
out general expressions which formally are the same for the various
types of magnets. Of course the values of certain coefficients
change from one type of magnet to another.
symbols is used hereafter.
The following list of
l.l Dimensions and geometrical parameters
a) Equivalent magnetic length = L
b) Average length of conductor in beam direction = K1L
c) Length of iron yoke = Ly= c1L
![Page 4: CERN/SI/Int. DL/70-10 BASIC EXPllliSSIONS POH EVALUATING ...cds.cern.ch/record/1462804/files/CERN-SI-INT-DL70-10.pdf · cern/si/int. dl/70-10 7.12.1970 basic explllissions poh evaluating](https://reader033.vdocument.in/reader033/viewer/2022060313/5f0b6a5b7e708231d4306866/html5/thumbnails/4.jpg)
Remark
- 2 -
d) Deflecting angle
e) Maximum required deflecting angle
f) Maximum beam dimension (horizontal)
g) Radial aperture ( equal to t~e
sagitta plus the beam diameter and margin)
h) Radial extension of coil
i) Vertical extension of finished coil
j) Vertical extension of pole
k) Gap height
1) Dimension of return yoke
m) Average length of conduc<:or due to "~~c
n) Radial width of conductor ir-c~uding
insulation
o) Height of conduccor including ir.z'"'lation
p) Effective conductor cross sec<:ion (taking
into account insu~ation and cooling hole)
q) Additional radial aperture for field
inhomogeneity and vac~ur:-,. cha:n.ber
r) Aspect ratio of the coil
= 8
= w a
= w c
= d = K7
h
= e ~ K8
h
= h
= a
= K3Wc
= cw
= ch
= K6CWCh
= K h 9
KlO K~,h
= = 7'-c It must be noted that in principle it is not correct to
assume the lengths under b) and c) above as si~ply
proportional to L. In fact both
L through expressions of the form
is shown in section 6. a) and b).
and c1
depend upon
or c1 = A ± ~' as it
1.2 Other parameters
a) Particle momentum
b) Number of turn
= p
= N
![Page 5: CERN/SI/Int. DL/70-10 BASIC EXPllliSSIONS POH EVALUATING ...cds.cern.ch/record/1462804/files/CERN-SI-INT-DL70-10.pdf · cern/si/int. dl/70-10 7.12.1970 basic explllissions poh evaluating](https://reader033.vdocument.in/reader033/viewer/2022060313/5f0b6a5b7e708231d4306866/html5/thumbnails/5.jpg)
- 3 -
c) Resistivity of conductor material (at working temperature)
d) Nominal field at center of gap (d.c. or
e) Current required for B (d.c. or peale)
f) Effective current density (d. c. or peale)
g) Saturation coefficient (where .!II is the
fraction of the current needed for the
ampere-turns in the iron) (d.c. or peale)
2. Active po~er
= Po
peale) = B
= I
= j
For all types of magnets, the resisoance of the coil is
given by
One can replace most of the !:lagne·o pararne-;;ers of (1) by
beam parameters in ~he following way :
(l)
W = (sagitta + beam diame"Cer) - margin for ::::.eld inhomogenei t.;· a max
+ K9
t
N NI Bh I=~= ~-'o
Incorporating (2), (3) and (4) into (1) and from P = RI2 ,
one has finally the expression for the d.c. or the peale power
( 2)
( 3)
(4)
![Page 6: CERN/SI/Int. DL/70-10 BASIC EXPllliSSIONS POH EVALUATING ...cds.cern.ch/record/1462804/files/CERN-SI-INT-DL70-10.pdf · cern/si/int. dl/70-10 7.12.1970 basic explllissions poh evaluating](https://reader033.vdocument.in/reader033/viewer/2022060313/5f0b6a5b7e708231d4306866/html5/thumbnails/6.jpg)
- 4 -
2p P = __ c e
'h (K + _!!!\ ll + J s l 8/ 0.3 (I. term)
~0
2 Pc r +- jh b
~o m \ _P~ ( + K h s + II. term)
9 / 0. 3L
(III. term)
The expression (5) is valid for all types of magnets, but
of course the coefficients Xi vary within different ranges for
various types.
(see Fig. lb)).
In particular K7
= 1 for window-frame magnets
... v.ne
The I. te= is concerned ·,vi th the power required for the
part of the coil parallel to the be~ and for the part of the end
connections correspondi~~ to the sagitta, the II. ter~ to the par~
of the end connections correspondir~ ~o the bean diameter ar.d to ~te
margin and finally '!:he ::r. ~er:~ -co "''e 'Jar-;; of the e!ld connections
corresponding to t~e coil radial ex~ension.
It is interestiY'_g to no1;e that in case of a long narrow
magnet not satura~ed (s = l), (5) tends to to the very simple for=
p 2 Pc
jh (, -'- ":r.' DA ::::-- ~
~0 '"¥1 3/ 0.3
which can be considered as the minimum power required to deviate by
an angle 9 a beam and momentw" p.
Introducing the numerical values for ~ and for o of o ·c copper at 30°C and usual units for the other parameters one has :
(5)
(6)
![Page 7: CERN/SI/Int. DL/70-10 BASIC EXPllliSSIONS POH EVALUATING ...cds.cern.ch/record/1462804/files/CERN-SI-INT-DL70-10.pdf · cern/si/int. dl/70-10 7.12.1970 basic explllissions poh evaluating](https://reader033.vdocument.in/reader033/viewer/2022060313/5f0b6a5b7e708231d4306866/html5/thumbnails/7.jpg)
- 5 -
P[KWJ = 29.44 {~2] h [mJ s (K1 + :m) J.93
[T.m] +
K + 23.43 ~ h [mJ
6 7
The relation (7) shows that, in order to obtain an
approximate evaluation of the power required to deviate a beam of
diameter bm and momentum p by an angle em' it is necessary to fix
only j and h and have a knowledge of the coefficients K. from ~
previous design and/or from some other considerations (see section 5).
To complete the electrical parameters, the expressions
for the voltage E and the current I are :
E = 2p NjL(K + em~+ 2p Nj(b + c l 8_,; c m
=~ l ......E.L I N h s 0.3L
i-1o
(8)
(9)
Expressions (8) and (9) contain in an important way actual
magnet parameters like N and L and therefore are of less immediate
use than (5).
Introducing the usual numerical values and practical
units, one has :
![Page 8: CERN/SI/Int. DL/70-10 BASIC EXPllliSSIONS POH EVALUATING ...cds.cern.ch/record/1462804/files/CERN-SI-INT-DL70-10.pdf · cern/si/int. dl/70-10 7.12.1970 basic explllissions poh evaluating](https://reader033.vdocument.in/reader033/viewer/2022060313/5f0b6a5b7e708231d4306866/html5/thumbnails/8.jpg)
- 6 -
e + _2!!.\ +
8
I [AJ -- 0.796 ~ h [mJ s o:~L [TJ x 106
In case of a pulsed magnet, the active power P can be
expressed by :
The peak power P and the peak current I are given
respectively by (5) and (9). As to the voltage E, the expression
(10) gives only the peak resistive part. The inductive part will
be treated in section 5.
3. Volume of conductor
For all types of magnets, the volume of conductor is
(10)
(11)
![Page 9: CERN/SI/Int. DL/70-10 BASIC EXPllliSSIONS POH EVALUATING ...cds.cern.ch/record/1462804/files/CERN-SI-INT-DL70-10.pdf · cern/si/int. dl/70-10 7.12.1970 basic explllissions poh evaluating](https://reader033.vdocument.in/reader033/viewer/2022060313/5f0b6a5b7e708231d4306866/html5/thumbnails/9.jpg)
write
one has
- 7 -
By using the relations (2), (3) and (4), we can also
e V = .1... 1;. hs(K + .2!!.\ ..J/JL +
c ~ J . 1 8/ 0.3 0
Introducing the numerical values and practical units,
1 ( 6m\ .J&_ [ J +
1.59 -j""['""mm"'A""'2
]"'" h [m] s K1 + ""8> 0 _3 T.m
+ 1.59 ~~ h [m] J-
mm2
s (b + K h-, [ml ...J?.L [Tl + m 9 . - 0. 3L -
1 ...:l + 1.27 13]l K K h [m]
j2 ...L 6 7 4
mm .J
(12)
![Page 10: CERN/SI/Int. DL/70-10 BASIC EXPllliSSIONS POH EVALUATING ...cds.cern.ch/record/1462804/files/CERN-SI-INT-DL70-10.pdf · cern/si/int. dl/70-10 7.12.1970 basic explllissions poh evaluating](https://reader033.vdocument.in/reader033/viewer/2022060313/5f0b6a5b7e708231d4306866/html5/thumbnails/10.jpg)
- 8 -
4. Volume of yoke
The dimension a of the yoke (see Fig. 1) can be expressed
in terms of W and W by means of a c
a = K fw + w' 4 a c,
(\1 w \if
a = K4 + c a 2lC +1,..
"'
w r\'1
~
and K4 c a = + 2(2K 3 +1)~ - a
{}
for windor1-fre.me magnets with one or two return yokes
for pole magnets with two return yokes
for pole magnets with one return yoke
The different types of ~agnets of Fig. l require slightly
different expressions for the yoke vol~e.
* The (2K8
+1) does not correspond to e. rigorous treatment of the flux
passing through the coil, but it is simple approximation which 'N
improve3 with increasing c. h
4.1 Volume of yoke for magne-cs witb. two return yokes
(14)
(15)
This expression is valid for both the window-frame
magnets (K8 = 0) and for the pole magnets (K8 ~ 0).
![Page 11: CERN/SI/Int. DL/70-10 BASIC EXPllliSSIONS POH EVALUATING ...cds.cern.ch/record/1462804/files/CERN-SI-INT-DL70-10.pdf · cern/si/int. dl/70-10 7.12.1970 basic explllissions poh evaluating](https://reader033.vdocument.in/reader033/viewer/2022060313/5f0b6a5b7e708231d4306866/html5/thumbnails/11.jpg)
- 9 -
4.2 Volume of yoke for C magnet with pole
+C1
LK4(2K
8+l\,/ (wa + We :'\ + 2C LK h W P 4K8+2/ 1 s a
4.3 Volume of yoke for C magnet of window-frame type
By using the usual expressions(2), (3) and (4), it is
possible to work out general expressions containing the beam
parameters.
nowever, such expressions are rather long and are not
given here for simplicity. It is easy in any given case to replace
the magnet parameters by actual values calculated by means of (2),
( 3) and ( 4).
5. Stored energy
In the case of pulsed magnets one has also to evaluate
the stored energy \VB and its consequences, the inductance LB and the
time constant T·
WB = ~ fv BHdv
(16)
(17)
![Page 12: CERN/SI/Int. DL/70-10 BASIC EXPllliSSIONS POH EVALUATING ...cds.cern.ch/record/1462804/files/CERN-SI-INT-DL70-10.pdf · cern/si/int. dl/70-10 7.12.1970 basic explllissions poh evaluating](https://reader033.vdocument.in/reader033/viewer/2022060313/5f0b6a5b7e708231d4306866/html5/thumbnails/12.jpg)
- 10 -
LB 2 WB
= 12 (18)
2 WB ,- = p
Where v is all the volume in whicl1 B and H are not nil. This volume
inclu.des both the air volume of the aperture L'4'1d the yoke itself. The
energy stored in the latter is usually rather small (- 0 for ~ ~ ro)
compared to the one stored in the air, so that a rather rough appro
ximation is sufficient for the purpose of this report. The following
expressions apply to the various types of magnets.
5.1 Stored energy for magnets with two return yokes
1
2~ 0
K h\ (pe \2 + 9 ) \!}.3)
(19)
where the last term represents the energy stored in the yoke and
for window-frame magnets. L. is the average flux line in the ~
yoke and is given by :
+ 2 w c
where, as usual, K8 = 0 for window-frame magnets.
5.2 Stored energy for magnets with one return yoke
+ _1_ h r;; +K j;\ 2~ L ~m 9'/
0
( .£L_.}2 + \jl.y
(20)
![Page 13: CERN/SI/Int. DL/70-10 BASIC EXPllliSSIONS POH EVALUATING ...cds.cern.ch/record/1462804/files/CERN-SI-INT-DL70-10.pdf · cern/si/int. dl/70-10 7.12.1970 basic explllissions poh evaluating](https://reader033.vdocument.in/reader033/viewer/2022060313/5f0b6a5b7e708231d4306866/html5/thumbnails/13.jpg)
b ';· p 1 t _s_~ __ :z::£~
- 11 -
W = - 1- h ....!!!.fP~2\ + ..1.._ .£ ft +K h\ .£L + e 2 a 02 B 2~ 8 ~ 2~ L ~m 9~ 0.3
0 0
+ 2W c
(23)
(24)
II.B. The choice of j for a pulsed magnet is not only related to cost
considerations (see par. 7), but also to an appropriate value
for the time constant T· In fact j can be high8r, the magnet
itself smaller and T also smaller than for a d.c. magnet.
6· Possible values for the coefficients c1
and Ki
a) c1 , ratio of the core length to the magnetic length, is
obtained with good approximation by means of
magnetic length ~ core length + gap
![Page 14: CERN/SI/Int. DL/70-10 BASIC EXPllliSSIONS POH EVALUATING ...cds.cern.ch/record/1462804/files/CERN-SI-INT-DL70-10.pdf · cern/si/int. dl/70-10 7.12.1970 basic explllissions poh evaluating](https://reader033.vdocument.in/reader033/viewer/2022060313/5f0b6a5b7e708231d4306866/html5/thumbnails/14.jpg)
- 12 -
b) K1
, ratio of the average conductor length in the beam
direction to the magnetic length, is in general rather
c)
d)
close to c1
• From existing designs, one can assume :
K~, ratio of the average conductor lensth duo to IV toW ~ c c
itself, depends on the eoil design .. .For "flat" coils
(generally possible in pole "'"gnets) it tends to be smaller
than for coils ·.vi th 11 s2ddle-s11aped 11 ends (windo·.v-i'rarne r::.e.~:::.e-::=
and pole magnets rri tL t''e coil ·:rinaovr couplet ely filled).
One can assume the followir~ :
K4
, relates
where K3
is
K3
= 2 + 0.2 for "flat" ends
K3
= 3 ~· 0.8 for ''sadale-shaped 11 ends
a to W and \'1 througL the relations (14), a c defined ur:der ,g) below and is nil for ·.vindow-
frame m~g:1e ts.
The conservation of f2~x in th8 magnetic circuit requires
that
K4 0.5 B --
B. l
nagnets with two return yokes
K4 B
- B. l
magnets with one return yoke
where B. is the average field in the mediru1 plane of the l
return yoke(s).
![Page 15: CERN/SI/Int. DL/70-10 BASIC EXPllliSSIONS POH EVALUATING ...cds.cern.ch/record/1462804/files/CERN-SI-INT-DL70-10.pdf · cern/si/int. dl/70-10 7.12.1970 basic explllissions poh evaluating](https://reader033.vdocument.in/reader033/viewer/2022060313/5f0b6a5b7e708231d4306866/html5/thumbnails/15.jpg)
- 13 -
e) K6 , ratio of the effective copper surface to the overall
cross-sectional surface of the coil. It depends on the
voltage to be applied to the magnet and, in existing
CERN designs, varies between 0.5 and 0.7.
It is a rather important coefficient to be watched since
a too great conservatism in the insulation thickness
(small K6~ leads either to a too high current density and
power consumption or to a bulkier magnet, especially in
the case of window-frame magnets.
In view of this it is suggested to adopt
f) K7
, ratio of the total vertical extension of the coil to
the gap, depends on the type of magnet (pole or window
frame). One has typically :
for window-frame magnets
K7
~ 2K8
for pole magnets in which the coil is split in
two parts (upper m,d lower pancake) and the
end connections are 11 flat 11 •
for pole magnets with "saddle-shaped" ends
g) K8 , ratio of the pole height to the gap, is obviously
nil in case of window-frame magnets.
Instead of fixing a value for K8 , it is more convenient
for the optimizRtion procedure which follows to fix a value
![Page 16: CERN/SI/Int. DL/70-10 BASIC EXPllliSSIONS POH EVALUATING ...cds.cern.ch/record/1462804/files/CERN-SI-INT-DL70-10.pdf · cern/si/int. dl/70-10 7.12.1970 basic explllissions poh evaluating](https://reader033.vdocument.in/reader033/viewer/2022060313/5f0b6a5b7e708231d4306866/html5/thumbnails/16.jpg)
- 14 -
which in turn gives K7
and K8 (through relations such as
K7
= 2K8 and K7
= 2K8 + l of f) above). In this case K7
and
K8
vary with the para;:ceters j, s and B and depend on the
value of K6 .
h) K9
, ratio between the total margj_n included in the horizontal
aperture (for field inhomogeneity and vacuum chamber) to the
gap, depends on the type of magnet, on the required field
accuracy and on the gap icself.
field accuracy of 10-3
One has generally for a
K9 -- 0.5 l.O for window-fra..11e
K9 = 1.0 .:. 1.5 for pole m.agne'ts
The smaller value is valid for relatively 1 h ~ 0 10 ) - -1 ... ~ ..... l l a'<;l ~ /. ::: ~ e::.. • m , ·.vnl e ror ...,.~.3-.J.. ..... er 0 c..p.:;, \n
K9 is more appropriate.
7. A possible optimi~ation procedure
oagne-:;s
large gaps
0.05 ::.) the
The basic specifications required for initiating the
actual design of a magnet are :
a)
b)
c)
d)
Bending power
Maximum bending angle
(irrespective of momentum)
_Vertical gap
Maximum beam dimension
(in the direction JL to B)
BL
h
b m
[T.ml
[radian J
[mJ
[mJ
higher
![Page 17: CERN/SI/Int. DL/70-10 BASIC EXPllliSSIONS POH EVALUATING ...cds.cern.ch/record/1462804/files/CERN-SI-INT-DL70-10.pdf · cern/si/int. dl/70-10 7.12.1970 basic explllissions poh evaluating](https://reader033.vdocument.in/reader033/viewer/2022060313/5f0b6a5b7e708231d4306866/html5/thumbnails/17.jpg)
e)
f)
- 15 -
Field accuracy in the beam
region
Foreseeable utilization time
liB B
0
T [hour J
If free from limitations in cross-section, length, weight,
etc., the magnet designer can then set up an optimization procedure
With the aim of finding a magnet system (magnet itself, power supply
and distribution, and cool:'.ng) of miniuum cost, taking also into
account the running expe:.diture.
The overall cost of a ::-.agne·;; sys"';e::l can be sul>divided
then into equipment cost and running co2: .. 7hese t·.vo costs ~re rather
different in nature sinca tha former is a capital investe::~ent to be
paid in & relatiyely shor·t time (ore, or t·::o years), while the latter
is spread over the entire working perie>d a:· ,,.,e equipment and, at
the Boment of forecast, :nay contair. some uncer-:;ainty with regard to
the actual utilization time T and other factors. The equipment cost
Me can be expressed by
M - M + M + l\ + '! + '·' e 1 2 '3 ·· 4 ·"5 (25)
where Ml = cost of po·uer supp2.y and associated equipr::ent
M2 = cost of finished coil :1ounted on the yoke
113 = cost of finis:1ed yo:ce
M4 = cost of a. c. and d.c .. power distribution
M5 = cost of cooling
The running cost is given essentially by :
M6
= cost of electricity for the power supply,
the a.c. and d.c. distribution and the
cooling.
By restricting ourselves to the case of d.c. magnets, the v~rious
M1
can be expressed as follows.
![Page 18: CERN/SI/Int. DL/70-10 BASIC EXPllliSSIONS POH EVALUATING ...cds.cern.ch/record/1462804/files/CERN-SI-INT-DL70-10.pdf · cern/si/int. dl/70-10 7.12.1970 basic explllissions poh evaluating](https://reader033.vdocument.in/reader033/viewer/2022060313/5f0b6a5b7e708231d4306866/html5/thumbnails/18.jpg)
- 16 -
7 .1 M1 - cost of power supply and associated equipL1ent
If the power 3upply feeds only the magnet i.n question,
the cost can be expressed by :
(26)
where H01 = cost independent froe1 P (in a certain power range).
It includeo the necl1anicc.l structure, t~:.e basic
cubicle equipment, the electronics, t!:e re::J.ote con-
wri"te
troJ s, etc.
m1
= cost/kw
ai) = multiplication fac"';or in units of [~;~-l of tl:.e
magnet power?, to obtain ~he apparent po~er on
the e .• c. side.
If the power supply feeds .. ~ :: . .::.;~e v2 in serie 2, :::.:.e ca...l'l
' ''. +m..<a?
.L '- n
M01 , m1
and ~depend on the type of rec~ification used :s or 12
phe.se), on the precision ·.van ted a.nd en "tile power ra....~.ge. rt depends
in addition on t!-.e distance between power supply and mR.gnet and
(slightly) on 'he ntmber of magnets fed.
7.2
where
hl - cosc of finished coil 2
For sake of simplicity, this cost can be expressed by
= cost/m3 of conductor in finished coil
(27)
(28)
![Page 19: CERN/SI/Int. DL/70-10 BASIC EXPllliSSIONS POH EVALUATING ...cds.cern.ch/record/1462804/files/CERN-SI-INT-DL70-10.pdf · cern/si/int. dl/70-10 7.12.1970 basic explllissions poh evaluating](https://reader033.vdocument.in/reader033/viewer/2022060313/5f0b6a5b7e708231d4306866/html5/thumbnails/19.jpg)
- 17 -
m2 depends on the insulation technique adopted, on the form of the
coil, e.g. with "flat" or "saddle-shaped" ends, and on the number of
coils to be made.
7.3 M3
-cost of finished yoke
As for M2
, this cost can be expressed by
(29)
where : m3
- cost/m3 of iron in finished yoke.
m3
depends on the precision required, on the type of core (solid or
laminated), on the type of steel and on the number of cores to be
made.
7.4 114
- cost of a.c. and d.c. power distribution
This cost 2 ) includes all equipment and installations
related to the a.c. and d.c. distribution, such as cables, substation,
etc. It can be expressed for simplicity by
(30)
where : m4
~ cost/kw
m4
depends on the layout adopted (power supp1ies concentrated in
one location or installed near to the magnets), on the flexibility
required (power reserve in the cabling) and on the current level.
7.5 M5
-cost of cooling
This cost 3) includes the central cooling installations
and the distribution system. Again for simplicity it can be expressed
by :
![Page 20: CERN/SI/Int. DL/70-10 BASIC EXPllliSSIONS POH EVALUATING ...cds.cern.ch/record/1462804/files/CERN-SI-INT-DL70-10.pdf · cern/si/int. dl/70-10 7.12.1970 basic explllissions poh evaluating](https://reader033.vdocument.in/reader033/viewer/2022060313/5f0b6a5b7e708231d4306866/html5/thumbnails/20.jpg)
- 18 -
M5 = m5 P
where : m5
= cost/kw
m5 depends on the type and total capacity of the plant and on the
layout of the experimental area.
7.6 M6 - cost of electricity
( 31)
It includes the cost of electricity for running the power
supply (including a.c. and d.c. distribution systems) and the cooling.
ct can be expressed by :
(32)
where m6 - cost/kwh of the electricity
S = correction factor for the magnet power P 1 which takes
into account the power cost in the rectifier itself
and in the a.c. and d.c. distribution systems, the
power necessary to run the cooling system, and a
posstble reduction factor since the magnet may not
be excited always at full power.
It is important to note that the cost M6
is rather different in nature
from M • While the latter is a firm investment cost to be paid in a e relatively short time (one or two years), the former is spread over
many years (e.g. ten) and it has not the same degree of certainty
(the time T and the S are somewhat uncertain). In order to compare
it toM the minimum that should be done is to capitalize it to the e moment of the investment by applying a suitable interest factor
which could also be included in S.
7.7 Cost normalization
It appears rather difficult to establish a precise set of
values for most of the costs Mi. In fact, besides the implications
![Page 21: CERN/SI/Int. DL/70-10 BASIC EXPllliSSIONS POH EVALUATING ...cds.cern.ch/record/1462804/files/CERN-SI-INT-DL70-10.pdf · cern/si/int. dl/70-10 7.12.1970 basic explllissions poh evaluating](https://reader033.vdocument.in/reader033/viewer/2022060313/5f0b6a5b7e708231d4306866/html5/thumbnails/21.jpg)
- 19 -
of a particular design, one has to take into account the cost
variation from year to year and the fluctuations of the economy
(expansion, recession) which have been recently even more important
than the cost variation itself, calculated according to the usual
formulas. As far as the equipment cost !II is concerned it seems e
reasona.ble to adopt a normalization which gives the correct relations
between the various Mi but leaves undetermined the absolute level
in actual money.
By doing so, it is obvious that the results of the opti
mization procedure to minimize the equipment cost remain valid until
a modification occurs in the relative cost of the various items.
If one wants however to determine the actual cost in money, the
value of "unity" in the normalization has to be assessed following
the economic conditions, price variation formulas, etc. For the
running cost, since the cost of electricity in a given laboratory
is rather well known over a number of years, its normalization
implies that "unity'' has to be specifically stated. This will
be done as an example in 7.8. Of course the optimization on the basis
of an essentially variable cost, such as M , and of a more stable e cost, such M6 , may require more frequent revisions than for Me alone.
7.8 Example of application
To illustrate a possible application, the following case
is treated numerically for a H magnet :
.E.L = 5.0 Tm e = 0.05 rad h - 0.05 m 0.3 m
b = 0.0(-) m f::,B
-· l0-3 T -- 30.000 hours m B
0
Most of the coefficients K. are chosen according to l
current pratice as follows :
![Page 22: CERN/SI/Int. DL/70-10 BASIC EXPllliSSIONS POH EVALUATING ...cds.cern.ch/record/1462804/files/CERN-SI-INT-DL70-10.pdf · cern/si/int. dl/70-10 7.12.1970 basic explllissions poh evaluating](https://reader033.vdocument.in/reader033/viewer/2022060313/5f0b6a5b7e708231d4306866/html5/thumbnails/22.jpg)
- 20 -
for 11flat 11 coil connections
for "saddle-shaped" coil connections
s and K4
, which depend on Bi' are taken to vary with B following
a parabolic law.
this corresponds to :
B 0.8 for B l T; B. = -· ~
B 1.2 for B 2 T. B. - =
l
For the saturation parameter s, we take
s = 1 for B ~ 1.25 T
s = for 1.25 < B < 2 T
which gives s = 1 for B - 1.25 T
and s - 1.2 forB= 2 T.
According to 6 f) and g), we have taken
which in turn gives
= K7 2
for "flat" connections
![Page 23: CERN/SI/Int. DL/70-10 BASIC EXPllliSSIONS POH EVALUATING ...cds.cern.ch/record/1462804/files/CERN-SI-INT-DL70-10.pdf · cern/si/int. dl/70-10 7.12.1970 basic explllissions poh evaluating](https://reader033.vdocument.in/reader033/viewer/2022060313/5f0b6a5b7e708231d4306866/html5/thumbnails/23.jpg)
- 21 -
__ K7-l K
8 2 for •saddle-shaped'' connections
7.8.1 Cost coefficients
For the equipment cost M , the following normalized e
coefficients are used :
1.35 for n = l
i) MOl -- O.'JO ml - 0.001 C{ =
1.1'7 for n = 4
which gives
= 0.50 + 0.00135 P [kwl for n = l
= 0.125 + 0.00117 P~wJ for n- 4
ii) M2 = 4 V 0 ~3]
iii) M3 - 0.4 V [m~ y
iv) M4 ·- 0.003 p [!r~
v) M5 =o.oo2PH
Por the running cost, two values have been used
-7 = 3 .10 TP !}:wl~
and
(32)
The former corresponds closely to the present price paid
by CERN and ~ = 0.5.
N.B. This set of normalized costs is preliminary, it takes into
![Page 24: CERN/SI/Int. DL/70-10 BASIC EXPllliSSIONS POH EVALUATING ...cds.cern.ch/record/1462804/files/CERN-SI-INT-DL70-10.pdf · cern/si/int. dl/70-10 7.12.1970 basic explllissions poh evaluating](https://reader033.vdocument.in/reader033/viewer/2022060313/5f0b6a5b7e708231d4306866/html5/thumbnails/24.jpg)
- 22 -
account only current techniques used at CERN, and is based on the
result of the most recent tenders, which are all of the medium size
type (total weight s 1000 tons). These tenders show a considerable
increase with respect to large contracts of the years 1967 and 1968,
beyond what can be calculated from price variation formulas. To
translate the above normalized coefficients to real prices on the
basis of the above tenders, "unity" in the normalization oould
be as high as 105 Sw. Fr., for an order of only few hundred tons and
including new tooling.
sity j and
All computations were
the yoke length L (or y
performed taking the current den
the magnetic field B) as main A parameters. 'l'he former was made to vary between 2. 5 and 10.0 --2 ,
while for the latter values between 2.5 m (=:~ 2 T) and 5 m (=:~ T)
were considered. Figs. 2 through 10 concern a magnet with "flat"
end connections fed by its own power supply (not feeding any other
magnet).
Fig. 2 gives the power P as function of j for various yoke
lengths. It is seen that the major variation occurs with j,
but a certain variation also occurs with J, (or J3) in the y
sense that the smallec't B in the range considered gives the
smallest P.
Fig. 3 gives the copper volume V as function of j for various c
yoke lengths. Same remark as for Fig. 2.
- ~,ig. 4 gives the yoke volume v as function of j for various y
yoke lengths. It is seen that the decrease of vy with j is
much less pronounced than for v c and that there is a value of
L for which V is a partial minimu1u y y
irrespective A
of j. This
is illustrated by Fig. 5, for j = 4.5 --2 • mm
- ]'ig. 6 gives the equipment cost M as function of j and for e
![Page 25: CERN/SI/Int. DL/70-10 BASIC EXPllliSSIONS POH EVALUATING ...cds.cern.ch/record/1462804/files/CERN-SI-INT-DL70-10.pdf · cern/si/int. dl/70-10 7.12.1970 basic explllissions poh evaluating](https://reader033.vdocument.in/reader033/viewer/2022060313/5f0b6a5b7e708231d4306866/html5/thumbnails/25.jpg)
- 23 -
various yoke lengths. It is seen that there is a rather flat
minimum with respect to j for j = 7 -Az, but there is also a
minimum with respect to L for L = ~ (B "'1.25 T). The latter y y minimum is also rather flat, with the minimum cost increasing
by only ~ 3 % going from I· - 4 m (B ":! 1.25 T) to y min L - 3m (B ":! 1,64 T). y
- l•'ig. 7 gives the total cost M (inclusive of the electricity
cons1Unption for 30.000 hours) as function of j for various
yoke lengths Ly. Here the minimum with j is obviously more
pronounced than for the equipment cost alone. The minimum with
respect to L occurs also at L - 4 m (B ~ 1.25 T), but the y y
difference is rather minor in the range 3.5 m < Ly < 5m, namely
for ~ l T < B < ~ 1.4 T.
- Fig. 8 gives the breakdown of the total cost M as function of
j for a yoke length L -- 4m. y
-Fig. 9 gives the minimal total and equipement costs as function
of h for b = 0.08 m kept constant. m
Fig. 10 gives the same costs as ]'ig. 8 for a case in which
both h and b vary. m
Fig. ll gives the total cost M as function of j for variouo
yoke lengths r, , when the magnet is fed in series with three y
other equal magnets. The part M01 of the cost of the power
supply, which is independent of the power, is then shared
between four magnets. The minimal cost (j = 4-.5 A2
and
Ly ~ 4 m) decreases by ~ 22 % with respect to thiFcase of Fig.7.
- Fig. 12 gives the total cost M as function of j for various
yoke lengths L when using a cost per unit of electricity equal y to half that of Fig. 7 (this may be the case for certain Ame-
rican laboratories).
Fig. 13 gives the total cost M as function of j for various
yoke lengths L , when the window of the magnet is completely y
filled with the coil, requiring "saddle-shaped" end connections.
It is seen that the minimal cost is slightly increased compared
![Page 26: CERN/SI/Int. DL/70-10 BASIC EXPllliSSIONS POH EVALUATING ...cds.cern.ch/record/1462804/files/CERN-SI-INT-DL70-10.pdf · cern/si/int. dl/70-10 7.12.1970 basic explllissions poh evaluating](https://reader033.vdocument.in/reader033/viewer/2022060313/5f0b6a5b7e708231d4306866/html5/thumbnails/26.jpg)
- 24 -
to Fig. 7, if one assumes that the cost/m3 of these coils is
the same than :for coils with "flat" end connections. Since
this might not be completely true, it is probably fair to
say that the cost difference between the two cases may be
slightly larger than shown.
The above results suggest the following considerations
and guide-lines.
'Phe equipment
for j ';i 7 A2
, with
the range ~- 9 A2
j in the above r~e
of electricity
cost M (Fig.6) shows a rather flat minimum e
only minor variations for values of j in
. This gives the opportunity of choosing
taking also into account the consumption
= 5 A2
would lead
equipment cost
(Fig. 7). A value j
M8
and total cost M very~lose to their respective
mj.nimao
As to the yoke length
the m~n~mum occurs for L = y
L = 3 m (B ~ 1.64 T) leads y in the equipment ~ost M . A
e total cost is considered.
8. Conclusions
L (or field B), it ic seen that y 4 m (B ~ 1.23 T), but an
to an increase of only few percent
similar argument applies if the
This report should be considered only as an encouragement
to magnet system designers to take into account overall economical
considerations. It does not replace in any way the detail design
of a magnet, nor does it pretend to be accurate enough for certain
coefficients and for the price formulas.
are welcome.
Comments and criticism
In what follows, we attempt nevertheless to outline some
tentative conclusions, based on various expressions throughout the
report and on the example of 7.8, of course only from an economical
view-point.
![Page 27: CERN/SI/Int. DL/70-10 BASIC EXPllliSSIONS POH EVALUATING ...cds.cern.ch/record/1462804/files/CERN-SI-INT-DL70-10.pdf · cern/si/int. dl/70-10 7.12.1970 basic explllissions poh evaluating](https://reader033.vdocument.in/reader033/viewer/2022060313/5f0b6a5b7e708231d4306866/html5/thumbnails/27.jpg)
- 25 -
1'he power of a magnet syetetl is very important, because it
en':iers into the overa]l cost through two major items, tl:e power supply
and it8 auxiliaries, and t!:.e r..:onsumption of electriclty. ':'his is
particularly true in CEH!I because of' ·che relatively higr, cost of
electricity. Obviously, one can give a different weight to the cost
of the equipment, to be paid in a relatively short time, and to the
cost of electricity, which initially has not the same degree of
certainty than the former and is distrib~~ed over a condiderably
longer time.
Fields outside the range 1,2 - 1,7 r appear disadvantageous,
even for the equipment cost alone; this is o:"' course even :lore true
if one includes the cost of electricity.
Certain aspects of the ~agnet desi6n deserve a special
attention, like the copper filling facto!' ;.;6
• I!l :'act the pov:er is
in firct <cpproximation inversely proportioc,al to K6
, all o-:o:Oer parameters
being equal. Altern:ltively, if j is kept co:cstant, a bigger ::agnet
results from a decrease of K6
. Relatively high values of K, are 0
obtained with a high current, a small nll!!lber of t-urns an6. a..11 insulation
thickness not overdesigned.
It is obviously advantageous to L~eed. ;·Jhenever possible sever3.l
magnets in series, since the psrt oi the _o~er supply coa~ i~de~e~de~~
from t!le power is rather important.
Finally, we draw the attention of ~he reader to the fact
that the actual methods of production of a Jagnet system ~ave an
important influence on the various coeffj_cients appearing in the
price formulas. This may be part of a separate study.
Acknowledgements
Vie wish to thank C. Iselin for some computation and many very
helpful discussions, and K. Braun, M. Georgijevic, R. Mosig and
H. Reitz for supplyinc; most of the infornation on the cos~ oo~ power
supplies and associate~ equipment.
![Page 28: CERN/SI/Int. DL/70-10 BASIC EXPllliSSIONS POH EVALUATING ...cds.cern.ch/record/1462804/files/CERN-SI-INT-DL70-10.pdf · cern/si/int. dl/70-10 7.12.1970 basic explllissions poh evaluating](https://reader033.vdocument.in/reader033/viewer/2022060313/5f0b6a5b7e708231d4306866/html5/thumbnails/28.jpg)
- 26 -
References
1) R, Mosig - d.c. and a.c. power of a rectifier set -
Private communication
2) H. Reitz -Private communication
3) K. Braun - Private communication
4) G. Hartwig - Cost calculation and optimization of bending
magnets and quadrupoles -
BSG - Notiz 70/5
IEKP, Karlsruhe
![Page 29: CERN/SI/Int. DL/70-10 BASIC EXPllliSSIONS POH EVALUATING ...cds.cern.ch/record/1462804/files/CERN-SI-INT-DL70-10.pdf · cern/si/int. dl/70-10 7.12.1970 basic explllissions poh evaluating](https://reader033.vdocument.in/reader033/viewer/2022060313/5f0b6a5b7e708231d4306866/html5/thumbnails/29.jpg)
"'
C><J >< " ___ __/ ···~
.c.
C><l C><J ~r. t-
a I We +- - w~ J We .. -~--- - a
··----~ ---
H Magnet with"flat" end connections of coils.
~
f----...!a!!...---4---'W!-'e'----+--·-'!.{a __ ~--+-----"W"'-e ---+--"-a --1
H Magnet with"saddle-shaped" end connections of coils.
FIG. 1a
![Page 30: CERN/SI/Int. DL/70-10 BASIC EXPllliSSIONS POH EVALUATING ...cds.cern.ch/record/1462804/files/CERN-SI-INT-DL70-10.pdf · cern/si/int. dl/70-10 7.12.1970 basic explllissions poh evaluating](https://reader033.vdocument.in/reader033/viewer/2022060313/5f0b6a5b7e708231d4306866/html5/thumbnails/30.jpg)
l I
<1l I I I
··-----·----~--~------~--
C><JI "0 ><: II .c
. ------ ---------·····
I a +- We +- Wa j We +----"
I
: Window- frame magnet (with one or two return yokes).
'-----···--·· ····--·---"""'' -· ----·
C magnet.
FIG. lb
![Page 31: CERN/SI/Int. DL/70-10 BASIC EXPllliSSIONS POH EVALUATING ...cds.cern.ch/record/1462804/files/CERN-SI-INT-DL70-10.pdf · cern/si/int. dl/70-10 7.12.1970 basic explllissions poh evaluating](https://reader033.vdocument.in/reader033/viewer/2022060313/5f0b6a5b7e708231d4306866/html5/thumbnails/31.jpg)
_Gnp !_·-~,_:_\iqht h.::: ~::~Orhtn Hcr1zcrr~ct LJC<1lll ~:Jirnt:T1~;ion brn !:.-= 60rnrn
_____ "F:!nt 11 co it r:n(1 cc;r-;neclions (i'or other co<-:~tficients ( l_ f'i._d_ 1')(!''('1'•1 C'lf'1'" <!po ·S'"Cl_i.('>fl '7 i'l) , •, •-. • . ,.-.! ~ , 1 , ~· .,lJ ~ "'-• <;__ ,_, " , '.- <
110 _;
Ly
2,5 100-
90 3
L
' ··:····l:-····:··~ +--------;__ i
: ... !. I T
·.:.:: ... :; ' '
10 -f--,--lt-:-:---'--------'-' ,-,--c---1 z;5 ' ! t T
J_
6 --;-----___1____;,--' __ L_• _,___:___j __ c..' - -+----:-'----- --{$>-
7 ___ , 8 9 10
l __ [ ______ f c i : _:_~ i
·:: L:: ·;: ·: ! :: · ;-. · t · · · · :. ·: :
--'-cl-~--"-· • :.Lc'
1 ·==· • Lcill_,j_c_i__:.:L..
'
I ., I
. . . . . . I . .
·- I
,. T- ---+-- -·-r j [A!rnrn2]
. T' . ····;·:·· .·:·-~-- . . , i. , , ___ :.:-J.:....::.i: .. : .. J:..:_~~;.I..:... .. ~L~:.:.J ... : . .:.:L.:.-~Ll_ _ _l_ __ ~- LFIG. 2
![Page 32: CERN/SI/Int. DL/70-10 BASIC EXPllliSSIONS POH EVALUATING ...cds.cern.ch/record/1462804/files/CERN-SI-INT-DL70-10.pdf · cern/si/int. dl/70-10 7.12.1970 basic explllissions poh evaluating](https://reader033.vdocument.in/reader033/viewer/2022060313/5f0b6a5b7e708231d4306866/html5/thumbnails/32.jpg)
0.25 -
0.15
0.1
0.05
vc
1 \ .... "I
• I I
\ r
.. '. \.
.) I
' ..... )
Vclurnc q::; funciion of _j unci vcrkY,JS. yoke~ ten!]ths Ly
sarnc· pol arne' t ·::·rs os in ·fig.2
Ly
............ J ' ..... ,
.. :J I
···········- : .... L :.:.i· __ , l- .: I
l___i_.:_L _ _:_;__· _j_ __ Li.. ... L.:__' ___ • __ L...:_i__,_.J ____ -J$>-
tcL2;L1cl ;_,j~JLcl J:j • .c: fl: .31 ~- ;U ••.•• : i Li0
J[Aimm']
![Page 33: CERN/SI/Int. DL/70-10 BASIC EXPllliSSIONS POH EVALUATING ...cds.cern.ch/record/1462804/files/CERN-SI-INT-DL70-10.pdf · cern/si/int. dl/70-10 7.12.1970 basic explllissions poh evaluating](https://reader033.vdocument.in/reader033/viewer/2022060313/5f0b6a5b7e708231d4306866/html5/thumbnails/33.jpg)
. --··· ~---
vv[m3]
I ····.·.[····· .· I . . . . . 1- · 0.9-~ -
i
I I I
I I
i I
: \
\ . \
'· \ : \
'
\
\~'.
\-' \~- \ .\
. \. "\ -\ ' \ '.\.··· \' '·-·
\ \ :\ \
\,, \ '
\ '· \. \.
\ \
. \
'\ ·\·· \
\
.\
'\. \~.
'\
'•
:::.(1 rriC' pc1
Ly
5
![Page 34: CERN/SI/Int. DL/70-10 BASIC EXPllliSSIONS POH EVALUATING ...cds.cern.ch/record/1462804/files/CERN-SI-INT-DL70-10.pdf · cern/si/int. dl/70-10 7.12.1970 basic explllissions poh evaluating](https://reader033.vdocument.in/reader033/viewer/2022060313/5f0b6a5b7e708231d4306866/html5/thumbnails/34.jpg)
i. ' )_:
1 , __ 8_ ~· I I
I o7 I ~ .. ! __ _ I I .. O.G .
L .. ! I ' I 0.5 -I I '. i I·· i: I ! i-' ' \--·.
l I I I ! ' . I . I I · 0.2 I ~--
1 .
t \f/i~·h
Volun .,-_,
Vy[rn~ -for q qivc;-rl _current cJ2n~1ity ]:
... ""· ··. : '_· .. ~:: N· : " ' ...... ' ' -...,
... -- ........... '<...-...:.._:~~~----------·
![Page 35: CERN/SI/Int. DL/70-10 BASIC EXPllliSSIONS POH EVALUATING ...cds.cern.ch/record/1462804/files/CERN-SI-INT-DL70-10.pdf · cern/si/int. dl/70-10 7.12.1970 basic explllissions poh evaluating](https://reader033.vdocument.in/reader033/viewer/2022060313/5f0b6a5b7e708231d4306866/html5/thumbnails/35.jpg)
2.3 -
2.2 -·
2.1 -
1.9 -
I 1.8 I·· I
I
1.7ll
1.6
1.5 -
1.4 -
1.2
·- \ \
\ \ \
\\ .\ \\ \ ,, .
\ \ "', ',
of j
Ly
- 3
LJ __ • _.]__· _l_ ___ l__:_,.L_ _, ___ , __ L ---'----1----~--'______J_-----j_ ____ j _____ L_L ___ ·_· ----~ 2,5 ~ .. 4 ? f;) 7 ' 8 . ~ . 10
.......... J[Aimm7]
FIG.6
![Page 36: CERN/SI/Int. DL/70-10 BASIC EXPllliSSIONS POH EVALUATING ...cds.cern.ch/record/1462804/files/CERN-SI-INT-DL70-10.pdf · cern/si/int. dl/70-10 7.12.1970 basic explllissions poh evaluating](https://reader033.vdocument.in/reader033/viewer/2022060313/5f0b6a5b7e708231d4306866/html5/thumbnails/36.jpg)
A
l I
2.'/ !~
2.6
v.
2.3 I
I
2.2 1--
1
2.1 ~-
2 -
1.9
1.8
1.7
1.6
\-·~
' \
\
\ \
\
\
\
I .. • ''); ;' '<) ,l !' ....
'•'¢-·---··--·-4. ··-' .. .-·
r· l
i t co•,;t '/i
I ."' ... ,\ ·, ('" ·-1 •. ·.• .. ·,·· ); , .•• ·.· .. • •. • •
• - .:~ ' ................ ·-... • _._._'. ------------------ ............................................... _........................ i
l
~-..-~·· . /
_.,,_ , ..
son ;c: pa
/ ' /
•") ,,:.,
/
' /
)
1.5 I L--_,' ____ .. L ____ __,_., ____ j _____ _, _____ J _____ ;__:,_L __ L_L_ • .. l._c.....L- .i ___ L_.....i....,..-_i _____ ,_--l'!>-
2.5 3 4 6 ) i $ 9 10 •
:FIG.7
. . . -. i . . .
! ... . 1 .. CL.C.C.C.L .... LI .•
I . .... , __ ,_L_ . L..c .• !. ..
1-,\l\•) \ ;, •
![Page 37: CERN/SI/Int. DL/70-10 BASIC EXPllliSSIONS POH EVALUATING ...cds.cern.ch/record/1462804/files/CERN-SI-INT-DL70-10.pdf · cern/si/int. dl/70-10 7.12.1970 basic explllissions poh evaluating](https://reader033.vdocument.in/reader033/viewer/2022060313/5f0b6a5b7e708231d4306866/html5/thumbnails/37.jpg)
1 -
08
0.7
OG -·
05
0.2
0.1
[·,1 i
( 'l (·< ~- i" e\ ,--~ t I. 7 c:~ rJ' Ll' .. ll ',\ 0 l 'J ···~-t ··-~'-· '-.
. \
\ \
\ \ ' \
\
\ \
' '·
)
' -\
·!·· ,...L _ _,__L__,__
25 4 :J.
net ion oi-
3ct rnl} po. ro
. ·l j_ _ _i_. _i_ __ i__• _L___;_'---J_ _ _,__ J __ __, __ j_ _____ ·-~·
5 6 .... 7 6 ... -~ 10
i[A!mrn 2] I_~_::J:.:J: __ [jj:JJ_:LI_:" ••.. IJ••. I_I __ •• ~·,G .• 8 . ' . . ' . i. -l . .
-· :~_..:__:.:..: ____ ~L ..:...·.:~ .• ;_! __ :,_.:._;__:.:J.:...:...:_~ .•. :J.:..__:~.;...:.__:_.:J_:_ __ :._:.~--~--- _____ .:...L ----. --· •
![Page 38: CERN/SI/Int. DL/70-10 BASIC EXPllliSSIONS POH EVALUATING ...cds.cern.ch/record/1462804/files/CERN-SI-INT-DL70-10.pdf · cern/si/int. dl/70-10 7.12.1970 basic explllissions poh evaluating](https://reader033.vdocument.in/reader033/viewer/2022060313/5f0b6a5b7e708231d4306866/html5/thumbnails/38.jpg)
I I I
'1 r I .T I
I I
2 -
. h-~ in i t h
Huritontnl l"rt dirt1t!n:;.ion·b~11 ::::b{)r-;i:n (con~~:.,
for other co::.:fricic:~n c1.nd pa.t-o1-r1{::\ters Se(:> .sect
I
' .. / I
/ -----l-1.
// /
···_z I
I
//
I i'-
1 /
I
~ Mfr) I
·-.. ' -c:: • 1 j:: lLJ J-\/iJ !ill ..
Ly::4._m
... --: --/~
I /
. ·i. t •
..... , .. .... ,._. . ' '
(...;....c_.;___j___. _• ___ j__ ____j ____ j _ _:_ __ • ____ L ____ :_____] __ : __ ! .•. _· _.;[_· . --'. --'-· .-'-... _.-;.!_' .-'---:-5.0. 50 70 1
. 80 9,0 . I . ! . . [ ] · ··· , .·: .
1 1 J ~ rnm
:,· ...... -. ·-·•-- ----- r i .... i,:: .· · :_ ..... · ;1
.....•... ' ... ) I ... ,1··· I
. . . .... ; . I . , .. : . ... _ .!. . . : . - . i . , . · · ·I . . . : . . . t • • :
l. ..• LL._L. ~l"l""L" ___ L.L_L;..J ••. ]FIG .. 9 __ ;__.: .J .. "~J.~_ .. LLL .. L.i .. L
;1t)
'/b)
![Page 39: CERN/SI/Int. DL/70-10 BASIC EXPllliSSIONS POH EVALUATING ...cds.cern.ch/record/1462804/files/CERN-SI-INT-DL70-10.pdf · cern/si/int. dl/70-10 7.12.1970 basic explllissions poh evaluating](https://reader033.vdocument.in/reader033/viewer/2022060313/5f0b6a5b7e708231d4306866/html5/thumbnails/39.jpg)
lZ::' c .. ond pcirornet~:r:;
3.0 -
i i
I
!. 2.0 ... i I I
I /""
. I ·; I
...... J
'/• I
// /
/
/ ./
I
/
/· /•
/ /
··/' .. /
;·· ·.I
I' ··I ' .
· .. ·.·;/·· I
;/ ... .... j ..
i i . . I
l . 7~ ! 1--~-T-- I
··/ /. · .. .
• ... /. /'
/ ... : .. /.
··; ....... , .
' ' ' . ' . . . . ' . • ' ' • t • < '
--/ ;
I
I . '/ .
~ Loll_' _j_ ~ L
I I 1.0 i
......... J.J_j ___ _j ____ __.I_. __ ·· -........Jc-~iO co 70 80
I• .Iii . ,' .so .J 65. ·. : . . I ' i. ,. :
I i' i ' ....• •.,_ ...•.. l.·.· .. •_··.······ · ... · .. ·_·l.·,_· .. ·,_·_·,·.,.·,.·.·.r, . T . IF I' G! 1 o· L .... ; .. .::~:.1/L.,:: ... L _ _ . . ... tL ... cLc .. C: 1. ' - J • _, .
80 ·. ··i . 95 110. I 1
. . . . . . i .
90 125 .
c .·_-,r ··-· ---- '···
j_::.: /)_~_) :\hnrn'·
I. y . I ! . I,.,
·tv~-:!.,.. rn
________ ; __ -----------~---{'~.~
h mm ··
' )lm[IYlm]
![Page 40: CERN/SI/Int. DL/70-10 BASIC EXPllliSSIONS POH EVALUATING ...cds.cern.ch/record/1462804/files/CERN-SI-INT-DL70-10.pdf · cern/si/int. dl/70-10 7.12.1970 basic explllissions poh evaluating](https://reader033.vdocument.in/reader033/viewer/2022060313/5f0b6a5b7e708231d4306866/html5/thumbnails/40.jpg)
A
l
2.2
2.1 -
2 -
1. 9 -
1.8 -
1.7 -
1.6 ·-
1.5 -
1.4
1.3
1.2 -
rr-n<:·~ii
• \ I
_\ \
\
\ \ ..
I I I
\
:' ''\, \
• \,
\
' \
ur;i t· ,)
~ ~-,_
'<·--
., ~
'· ·- '· -..v •• ,_
.J>----~
i '-1 : ... )
•\ ,:. ·'
'----- .... .(~
_c ____ ___L _____ _, _ _j ___ ..J ____ L ____ ;__:__j ___ j ____ '----'-----L-----'-----.J. __ ,__ __ L_ ________ i>.,._
25 3 /, 6 7 . 8 9 10
i[A/rnm]
![Page 41: CERN/SI/Int. DL/70-10 BASIC EXPllliSSIONS POH EVALUATING ...cds.cern.ch/record/1462804/files/CERN-SI-INT-DL70-10.pdf · cern/si/int. dl/70-10 7.12.1970 basic explllissions poh evaluating](https://reader033.vdocument.in/reader033/viewer/2022060313/5f0b6a5b7e708231d4306866/html5/thumbnails/41.jpg)
2.1 -
L9
.. 181
1.5
···\ \
r unii cf
_____ _t _____ .l 2,~) ~ ···-,·-~-- _I_ .•• J. ____ L __ j___ j . . . . 5 ' -6--"---~;-
FIG.12 i ..... ··- - L
~; Ct~:; in fie!.?
: .. ;·
l. " ")
3
![Page 42: CERN/SI/Int. DL/70-10 BASIC EXPllliSSIONS POH EVALUATING ...cds.cern.ch/record/1462804/files/CERN-SI-INT-DL70-10.pdf · cern/si/int. dl/70-10 7.12.1970 basic explllissions poh evaluating](https://reader033.vdocument.in/reader033/viewer/2022060313/5f0b6a5b7e708231d4306866/html5/thumbnails/42.jpg)
i I ' l
2.7
: 21 1- .
r 20r \ \·
\ ' \
.p-
I
\ \
'•
orn cil rn(_.··r! ~·:~ion
i C ,i C' i .. t t :·:.~ __ , ···'\ :;:.c,c tior1 1. C)
FIG.13
co1·1nc:c
h:::: FJO l!''rn rrtrn
. [A 21 j e,/ mrn J
; :,,1'<··~1· :.· .. t-.