Initial Calculations of Intrabeam Scattering life times in ELIC lattices by Betacool code Chaivat...

Initial Calculations of Intrabeam Scattering life times in ELIC

lattices by Betacool code

Chaivat TengsirivattanaCASA, Jefferson Lab

University of Virginia

The 4th Electron-Ion Collider WorkshopHampton University, VA

May 20,2008

3-9 GeV electrons3-9 GeV positrons

12 GeV CEBAFUpgrade

Pre-booster

Ion ring30-225 GeV protons15-100 GeV/u ions

ELIC Conceptual Design

Figure-8 Ring with 80 deg. Crossing (2100 m circumference)

Courtesy of Dr. Alex Bogacz

330 m150 m

80 deg

30 full cells8 empty cells 8 empty cells3 transition cells 3 transition cells

323.690

Mon Feb 25 09:33:57 2008 OptiM - MAIN: - N:\bogacz\Transfer\io_2m_dip_Ring\arc_pict.opt

40

0

50

BE

TA_

X&

Y[m

]

DIS

P_

X&

Y[m

]

BETA_X BETA_Y DISP_X DISP_Y

Figure-8 Ion Ring (half) - Lattice at 225 GeVCourtesy of Dr. Alex Bogacz

20.320

Mon Feb 25 09:42:31 2008 OptiM - MAIN: - N:\bogacz\Transfer\io_2m_dip_Ring\cell_in.opt

40

0

50

BE

TA

_X

&Y

[m]

DIS

P_

X&

Y[m

]

BETA_X BETA_Y DISP_X DISP_Y

Arc dipoles::

$Lb=170 cm$B=73.4 kG$rho =102 m

Arc quadrupoles:

$Lb=100 cm$G= 10.4 kG/cm

ELIC design parameters of ion ring

Courtesy of Dr. Yuhong Zhang

Parameter Unit Ion Ring

Beam energy GeV 225 150 100 30

e/A ring circumference km 2.1

Bunch collision frequency GHz 1.5

Number of particles/bunch 1010 0.42 0.4 0.4 0.12

Beam current A 1 1 1 0.3

Energy spread, rms 10-4 3

Bunch length, rms mm 5

Beta* mm 5

Horizontal emittance, norm m 1.25 1 0.7 0.2

Vertical emittance, norm m 0.05 0.04 0.06 0.2

Beam-beam tune shift (vertical) per IP

0.006 0.01 0.01 0.009

Peak luminosity per IP, 1034 cm-2 s-1 7.4 7.7 5.5 0.8

Number of IPs 4

Touschek Effect and Intrabeam Scattering

1. Touschek Effect- Large angle- transformation of a small transverse

momentum into a large longitudinal momentum, due to relativistic effect

- Both particles are lost immediately

2. Intrabeam Scattering- Small angle- Multiple scattering- Diffusion in all three dimension, change the

beam dimensions

BETACOOL code – LEPTA lab, JINR, Russia

Courtesy of Dr. Anatoly Sidorin

Lattice structure- ELIC lattice

Beam parameters- Set values

Ring parameters- Set values

Parameter Unit

Beam Energy GeV 30

Ring circumference m 2,100

Number of bunches 10,509

Horizontal rms emittance µm 0.006026

Vertical rms emittance µm 0.006026

Number of Particles 1.2 × 109

RF Voltage MV 100

Case I: Beam Energy 30 GeV

50 80 120 200 300 400 600 800 1600 3200100.00

1,000.00

10,000.00

100,000.00

1,000,000.00

247 230 221 215 212 210 209 208 207 207

11,486 10,676 10,265 9,957 9,811 9,740 9,671 9,637 9,588 9,565

3.39E+05 3.20E+05 3.10E+05 3.03E+05 3.00E+05 2.99E+05 2.98E+05 2.97E+05 2.96E+05 2.96E+05

30 GeV - Martini Numerical

Horizontal Vertical Longitudinal

numbrer of intervals in z direction

Lif

e ti

me

(sec

)

30 35 39 40 45100.00

1,000.00

10,000.00

100,000.00

1,000,000.00

260223 200 195 174

14,70512,605 11,312 11,029 9,804

1.34E+051.15E+05 1.03E+05 1.01E+05 8.94E+04

30 GeV - Martini Coulomb Logarithm


Coulomb logarithm number

Lif

e ti

me

(sec

)

Coulomb logarithm

max

min

ln lnr

r Definition :

max

min

2

20

the smaller of or

Debye length

the rms beam width

the classical impact parameter

4

D x

D

x

th

r

r b

qb

mv

Model Horizontal Vertical Longitudinal

Martini – Numerical 3.4 min 2.6 hr 82.3 hr

Martini – Analytical 3.4 min 2.6 hr 82.3 hr

Martini – Coulomb Log 3.4 min 2.6 hr 82.3 hr

Bjorken – Mtingwa 26.2 sec 26.2 sec 8.2 min

Case I: Beam Energy 30 GeV

Parameter Unit

Beam Energy GeV 100





Number of Particles 4 × 109

RF Voltage MV 350

Case II: Beam Energy 100 GeV

50 80 120 200 300 400 600 800 1600 3200100.00

1,000.00

10,000.00

100,000.00

428 398 383 372 367 364 362 360 359 358

3,703 3,445 3,314 3,216 3,170 3,147 3,126 3,115 3,100 3,092

1.71E+04 1.60E+04 1.53E+04 1.49E+04 1.47E+04 1.46E+04 1.45E+04 1.44E+04 1.44E+04 1.43E+04



number of intervals in z direction

Lif

e ti

me

(sec

)

30 35 39 40 45100.00

1,000.00

10,000.00

100,000.00

444381

342 333296

4,1853,587

3,219 3,1392,790

1.83E+041.57E+04

1.41E+04 1.37E+041.22E+04




Lif

e ti

me

(sec

)


Martini – Numerical 5.97 min 51.5 min 3.98 hr

Martini – Analytical 5.97 min 51.5 min 3.98 hr

Martini – Coulomb Log 5.97 min 51.5 min 3.98 hr

Bjorken – Mtingwa 5.39 min 27.7 sec 93.6 min

Case II: Beam Energy 100 GeV

Parameter Unit

Beam Energy GeV 150





Number of Particles 4 × 109

RF Voltage MV 520

Case III: Beam Energy 150 GeV

50 80 120 200 300 400 600 800 1600 3200100.00

1,000.00

10,000.00

100,000.00

746 694 668 648 639 635 631 628 625 624

5,652 5,258 5,058 4,909 4,839 4,804 4,771 4,755 4,732 4,720

2.45E+04 2.28E+04 2.19E+04 2.13E+04 2.10E+04 2.08E+04 2.07E+04 2.06E+04 2.05E+04 2.04E+04



Number of intervals in z direction

Lif

e ti

me

(sec

)

30 35 39 40 45100.00

1,000.00

10,000.00

100,000.00

771661

593 579514

6,3455,438

4,881 4,7594,230

2.64E+042.26E+04

2.03E+04 1.98E+041.76E+04




Lif

e ti

me

(sec

)


Martini – Numerical 10.4 min 78.7 min 5.68 hr

Martini – Analytical 10.4 min 78.7 min 5.68 hr

Martini – Coulomb Log 10.4 min 78.7 min 5.68 hr

Bjorken – Mtingwa 16.2 min 38.8 sec 4.90 hr

Case III: Beam Energy 150 GeV

Parameter Unit

Beam Energy GeV 225





Number of Particles 4.2 × 109

RF Voltage MV 100

Case IV: Beam Energy 225 GeV

50 80 120 200 300 400 600 800 1600 32001,000.00

10,000.00

100,000.00

1,4741,372 1,320 1,281 1,263 1,254 1,246 1,242 1,236 1,233

26,79924,925 23,976 23,266 22,930 22,767 22,609 22,532 22,420 22,367

4.38E+044.07E+04 3.92E+04 3.80E+04 3.75E+04 3.72E+04 3.70E+04 3.68E+04 3.67E+04 3.66E+04



Number of intervals in z direction

Lif

e ti

me

(sec

)


Martini – Numerical 20.6 min 6.2 hr 10.2 hr

Martini – Analytical 20.6 min 6.2 hr 10.2 hr

Martini – Coulomb Log 20.6 min 6.2 hr 10.2 hr

Bjorken – Mtingwa 32.9 min 80.0 sec 11.93 hr

Case IV: Beam Energy 225 GeV

30 100 150 225100.00

1,000.00

10,000.00

100,000.00

1,000,000.00

207

358

624

1,233

9,565

3,092

4,720

22,367

296,193

14,333

20,449

36,570

IBS life time vs Beam Energy - Martini model


Beam Energy (GeV)

Lif

e ti

me

(sec

)

30 100 150 22510.00

100.00

1,000.00

10,000.00

100,000.00

26

323

970

1,974

26 2839

79

491

5,614

17,622

42,950

IBS life time vs Beam Energy - Bjorken Mtingwa


Beam Energy (GeV)

Lif

e ti

me

(sec

)

Cooling rates

E-Cooling 30 GeV 150 GeV

Initial Cooling rate -1.1 x 10-3 -1.7 x 10-3

Cooling rate at Equilibrium -5.6 x 10-2 -1.7 x 10-2

Growth rates


30 GeV

Martini 4.8 x 10-3 1.0 x 10-4 3.4 x 10-6

Bjorken – Mtingwa 3.8 x 10-2 3.8 x 10-2 2.0 x 10-3

225 GeV

Martini 8.1 x 10-4 4.5 x 10-5 2.7 x 10-5

Bjorken – Mtingwa 5.1 x 10-4 1.3 x 10-2 2.3 x 10-5

Electron Cooling Rates

Summary

- Growth rates of new ring, 2100m, has been calculated.

- Horizontal and Longitudinal life times are agreed between different models.

- Discrepancy of life times in vertical (small) direction between models, trying to understand.

- Beam could be cooled by electron cooling for longer life times

Initial Calculations of Intrabeam Scattering life times in ELIC lattices by Betacool code Chaivat...

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