NLC Interaction Region Physics

Lecture # 13

Dr. Pisin Chen

MAY8,1998

3

I

t

Field of the Gaussian Beam

.

Assume Gaussian bunch:

Electric field is:

Bassetti-Erskine formula:

where W ( z ) = e-z 2 erfc(-iz)

Fx and Fv Fx and Fy 4k 2

1

-4 -2 A 2 4

Fx

-4 -L 2 4

WSigmaX

2 4 XISigmax

k 1 0

To find maximum fields:

O X

Locations of the maxima: 0.393 R2 = 1.307+

342

. .

I - I I I I I

. -._ ..e

T = IO

f m 25'

I ... - I 1 I 1 . 1 I I I I I 1

;I

0

- I

&?? 1 I I I I I I I I I I X

I I I I I I I 1 1 I

I I I I I I I I I 1 I I

5 -S 0 S -5 0 z/uz

Fig. 9(a). SimuLtion of the density diNibutioru during the c o W n of two Gaussian bcun, for D = 1.

..

.

I

344

- I I 1. IO T = 30 -

. - I :* .:.

I I I I 1 I I . . . . . .

. . - .C~ . . . I I

-. .c . . I ..- I

- I 0 -

- 0 0

W

- 0

- 0

N w 0 0

3.0

2.5

HD

2.0

I I l l l I I I I I l l l ~ i i I I I I

1.5

1 .o 1

10-88

10 100 6157A1

3 2

1

0.5

H D

0.1

0.05

0 1 3 4 5

,

U W

fom j d o r

2.0

1.5

n 1.0 h

0.5

0.0

t - 0

I c t + + t +

I

1 I

s - 0

Hd

- o o l t , 9 1 I I , I I , I , . I . I , * , , I . . , , I , , , 15 d -15

Figure 2. Net effect of disruption from analytic cdc. Hd=@st ) / (202)

Figure 3. The mmptual2disk model

Figure 4. zero, 1st and 2nd moment disruption &ea

L

t

0.00

-025

-0.W

-0 .m

-I m

-1.25 0 4 a0

-1.60 " " I ' " " " ' 1 ' ' ' 1 ' 2 J 4 !n Unltr OI dmm O m t -.t+r 1

D-&Ol,O.i,l.O rith A 4 . 0

figwe 5(a).Tradung Result with A=O.O

3

-4 O L - - --

4

0 -

-4

r-0.25

- 0.25 - - - - 1 I I I I

. O>

h

b* - -4

4 t - o

-4 O € -

i 0-88

0.50

0.75

1.00

1.25

-4 0 4 -4 0 4 6157A3

* i-4 J

,

6063A4 Positron

648 Bunch Troin

in

.LIZ- -.

- -.. P I .. P -*r

. -..*,' . .

- _

r

beans os a fwnction OF e e t s

Hd for X-offset

0.0 &l& 0 ' 4 3 4 5 x set sigma-x

Hd for Y-offset I I I I I I

0.7 t -

-

- - -

-

0.1

' 0 .0 015 l!O 1; 210 2 5 3.0 3.5

- -

y0rSa.rigrrp-Y

4

1

* L t t m SR: T >> I.

a

1

5

t

e-

\

7

n 3 L W

E w

Fig. 10. Sokolov-Ternov Spectrum Functioa

E' logw

. . \ . - - . .

\ Y

c

Fig. 11. Functions Uo, Ul and UJ. The crosses are the zppxirnzte foAnulas in Eqs. (3.62) a d (3.64).

ti T

Table 3: Effect d h s t r a h l u n g alone on e- and y energy spectra I 1 I 2 I 3 1 4 I - - 5

D-D wide bd

.075 1-3 i l 1.2 3-7 , 6 7

Design Class D-D nmv bd

-015 0.5 1.1 -60 0.9 1.2

Bcamstrahlung parameter T Mean e- energy loss (%)

Number of radiated yk/c' Mean photon energy (%)

1 e' enugy spread (%)

x d -- * 0 I O - ~

3

fI .- E

Palmer

15

13 ! Palmer F

-11 1 2.3 5-2 .YE C9 63

TESLA nrrw bd

.010 0.4 0.9 -I

.76 0.6 0.8

12-91 7063A.1

Figure 1: e+e- luminosity spectrum as a function of tfhe fractional electron energy (e- r) and the fractional positroan cmergy (e' z), for the strong beamstrahluna, X-band design (design 1). Linac energy spread is neglect.ed. The tdd luminosity is 10 fb-'. The bin size is -02 x .02.

9

lo-'l i o - *

- I 1 I lab, [f?#

10-4 0 0.2 0.4 0.6 0.8 . 1 .o PAC) L 4

I a + N vi -0

FIG. 2. Tao-dimensional plot of the e - e - differential lumi- nosity ( d ’ L e e + - / d x , d x , ) A x l Ax, per beam crossing as a function of the e + e - fractional energies, x ,xl, from computer simulation. The width of the bins is Ax, = b 2 = 0 . 0 2 . T h e ex- ample used is Palmer’s F design for a 0.5 TcV linear collider, where Y -0.12.

1

1

,

- Theoretical ( C h , 1492): II

c .I ..

c

c

10-3 - - c

Y

nl 0 4

'""'S I"""' I lliil"l l'""'' B"'"" ' - x

4 J

2

0 0 4

M I

0 4

X

I l l I I I

rl 11111I I I 1 1 1 1 1 I 1 I 1 1 1 1 1 I I I 1 1 1 1 1 ~ 1 I I 1 1 1 1 I I I 1

rn 4 0 0 4

0 4

0 4

4 I

0 4

c\I I

0 4

v 1

m I

0 4

0 4

00 d

X

d- ti

0

Pair Production Processes During Beam-Beam Interaction

In NLC . -

1. Coherent Pair Rahctbm /influence of the collective elecbromagnetic field of the beam)

B 'Y = 27- > 0.3

Bc B, = m 2 3 c / e 5 E 4.4 x 1oi3G

)I. hlcoherent Pair Production (two-body initial state)

Y < 0.3 1 B r e i t - W k k r Process

yy + e+e-

~ B W = -(In4 3 + 3 $Treyo 2 - 3 ( L - In 4)A2 8

re is the classical electron radius

..

2. Bethe-Heitler Process

e f y + e * + - e e

t

28 234 3 42

OBH = -aar:(L - -)A

3. Landau-Cifsh'rts Process

+ - + - + - e e + e e e e

a2rf 28 ~i 27

OLL = - ( -L3 - 6.59L2 - 11.8L + 104)

I

. . . . .

Fig. 14. The fuctioas qT) zad fl(T). The dashed and the dotted hts are the rsymptotic forms Eq. (4.83).

X=E&

Fig. 16. Eneigy spectiu,-i; of the cLscaCe OC beam- strahlung and coherect pair creation.

. , . , . . , .- . . . . . . . . . .. , . : ' . . . . . . . . _ . .. .

tl

Fig. 16: Scaled energy (x) distributions for OM of pair panicles created in the BH and LL processes for beam energy E&,,,,, = 500 GeV '.

13

c. 0 0

# of e*(e-)/bunch umcosain,g

CI 0 u

CI 0 c

0

e

8 " I

I

0

0 en 0

0 0

0 CI

0 0

cn 0 0 0

0 c.

Y cb

rl

.-

€6 G8V

r

S 70 /.V*rO

$00 /06

e'

%f& STRUCTURE

7-92

.

m 1 1

I

7

800

t

11-92

1 I I I 1 1 1 1 1 I I I 1 1 1 1 I 1 I I I I I I I 1 I l l

100 10’ -

103 104 7214A2

0 tot

m 0 3

0

m 3 0

104

n

W Q* 102

1 oo 1 0’

1 1-92

1 o2 103 104 721 4A6

11-92

20

15

10

5

0 1 o3

721 4A4

800

600

n 400

200

0

11 -92

1 o2 1 o3 7214A5

Fq. 6

1 o2

L .- a m > m u e P o - r U a = - r m

IO’

1 oo

IO-’

1 o-2

1 oo

lo-*

.. ,

I 0-4

11 -92

500 1000 Ecm (e +e- collider) (GeV)

5000 72 1 4A7

7

Ecm (yy collider) (GeV) 72 1 4A8

0 t

0

U t

11-92

lo-*

10-4

1 o-6

lo-’

10-3

I 0-5

10’ 1 o2

1 o3 721 4A9

t 0

m 1 n n

Lu 0 0

z U .

lo-’

I o - ~

I o - ~

10’ 1 o2 I I I 1 1 1 1 1 I I I I 1 1 1 I 1 I I I l l 1 l

1 TeV yycollider

io - *

. .

F

// /

I I 1 1 1 1 1 I t I 1 1 I I I I 1 1 1

IO’ 1 o2 1 o3 11-92 721 4A10

10’ Id 11-92 Ean(rr) (&v)

Tab1 1. Param ter- 3 Backgronds for 0.5 TeV Lin w C-Uiders - NLC

6.0

180

90

0.37

0.65

-

'300/3

10/0.1

o.Os/s.:

0.01/1.1

300J2.5

100

-

1.4

8.2

- DLC

2.4

50

172

0.27

2.1

-

a/= 500 16/1

0.70/8.i

0.03/0.:

246119

2.8

6.55

-

- TESLA

2.6

10

800

0.33

5.15

-

640/10(

lo00

10/5 - i.25p.

0.1/0.:

304150

4.2

11.1

- VLEPP

12

300

1

(0

-

m =I4

100/0.1

750

Linear Colliders CLIC JLC

2.7

1700

4

0.4

8.6

W/8

170

2210.16

1.3115

O.OS/l.Ol

4015.5

3.3

8.85

6.8

150

90

0.50

0.7

fE60/3

10/0.1

80

0.07/6

0.008/0.1

259 f 2.0

1.5

10.0

0.431-

0.008/-

1587/4

1.26

15.1

0.059

0.076

0.14

5.1

8.2

- 0.16

0.35

0.36

4.6

9.4

0.043

0.071

0.0s

3.1

4.0

0.15

0.15

0.05

1.0

1.1

~~ ~

0.095

0.096

0.03

0.S4

0.93

3.2

0.03

0.10

0.31

- -

0.031

0.065

0.14

5.8

9.9

54.6

1.53

1.61

3.89

- -

-

c 23.4 4.8 1564

45.5

5.s3

114.S

-

-

14.0

0.29

0.43

1.14 -

nThad

N j e t ( p , = 5GeV)[10e2]

Njet(p* = 10GeV)[10-4'

1.35

5.97

17.06

~

0.06

0.22

0.6s

1