initial calculations of intrabeam scattering life times in elic lattices by betacool code
DESCRIPTION
Initial Calculations of Intrabeam Scattering life times in ELIC lattices by Betacool code. Chaivat Tengsirivattana CASA, Jefferson Lab University of Virginia The 4 th Electron-Ion Collider Workshop Hampton University, VA May 20,2008. ELIC Conceptual Design. Ion ring 30-225 GeV protons - PowerPoint PPT PresentationTRANSCRIPT
Initial Calculations of Intrabeam Scattering life times in ELIC
lattices by Betacool code
Chaivat TengsirivattanaCASA, Jefferson LabUniversity 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
400
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
400
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
Life
tim
e (s
ec)
30 35 39 40 45100.00
1,000.00
10,000.00
100,000.00
1,000,000.00
260 223 200 195 174
14,705 12,605 11,312 11,029 9,804
1.34E+05 1.15E+05 1.03E+05 1.01E+05 8.94E+04
30 GeV - Martini Coulomb Logarithm
Horizontal Vertical Longitudinal
Coulomb logarithm number
Life
tim
e (s
ec)
Coulomb logarithm
max
min
ln ln rr
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
qbmv
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
Ring circumference m 2,100
Number of bunches 10,509
Horizontal rms emittance µm 0.006511
Vertical rms emittance µm 0.0005581
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
100 GeV - Martini Numerical
Horizontal Vertical Longitudinal
number of intervals in z direction
Life
tim
e (s
ec)
30 35 39 40 45100.00
1,000.00
10,000.00
100,000.00
444381 342 333 296
4,1853,587 3,219 3,139 2,790
1.83E+041.57E+04 1.41E+04 1.37E+04 1.22E+04
100 GeV - Martini Coulomb Logarithm
Horizontal Vertical Longitudinal
Coulomb logarithm number
Life
tim
e (s
ec)
Model Horizontal Vertical Longitudinal
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
Ring circumference m 2,100
Number of bunches 10,509
Horizontal rms emittance µm 0.006220
Vertical rms emittance µm 0.0002488
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
150 GeV - Martini Numerical
Horizontal Vertical Longitudinal
Number of intervals in z direction
Life
tim
e (s
ec)
30 35 39 40 45100.00
1,000.00
10,000.00
100,000.00
771661 593 579 514
6,3455,438 4,881 4,759 4,230
2.64E+042.26E+04 2.03E+04 1.98E+04 1.76E+04
150 GeV - Martini Coulomb Logarithm
Horizontal Vertical Longitudinal
Coulomb logarithm number
Life
tim
e (s
ec)
Model Horizontal Vertical Longitudinal
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
Ring circumference m 2,100
Number of bunches 10,509
Horizontal rms emittance µm 0.005194
Vertical rms emittance µm 0.0002078
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
1,474 1,372 1,320 1,281 1,263 1,254 1,246 1,242 1,236 1,233
26,799 24,925 23,976 23,266 22,930 22,767 22,609 22,532 22,420 22,367
4.38E+04 4.07E+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
225 GeV - Martini Numerical
Horizontal Vertical Longitudinal
Number of intervals in z direction
Life
tim
e (s
ec)
Model Horizontal Vertical Longitudinal
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
14,33320,449
36,570
IBS life time vs Beam Energy - Martini model
Horizontal Vertical Longitudinal
Beam Energy (GeV)
Life
tim
e (s
ec)
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
Horizontal Vertical Longitudinal
Beam Energy (GeV)
Life
tim
e (s
ec)
Cooling ratesE-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 ratesHorizontal Vertical Longitudinal
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