Beam dynamics calculations with MADX for SIS100

including “frozen BB” Sp-Ch

Valery KAPIN

ITEP , Moscow

GSI, 24-Mar - 2009

kapin@itep.ru

Two subjects for 6-week visit

“DA with Octupoles (for Landau damping) in SIS100”

=> report

“Benchmarking of sp.-charge induced loss in SIS100 ring”

=> PAC’09 paper

Benchmarking SIS18 steps 1-5 for 2D

• 1) Benchmarking of the Phase Space

2) Benchmarking of the Tunes versus particle

amplitude. Sextupole OFF.

3) Benchmarking of the Tunes versus particle

amplitude, with sextupole ON.

4) Benchmarking of the Tunes versus particle amplitude, with sextupole ON

5) Benchmarking of phase space with space

charge and sextupole on at Qx = 4.3504

DA of SIS100 study following GF-report

• Systematic and random errors in D & Q

• RMS closed orbit – 1.5/1.0 mm

• + Octupoles for Landau damping

Octupoles OFF => GF-report

Param 2a

syst. err ON

rand. errors

OFF

C.O.errors

OFF

DAave/min 4.2/3.9

+Sp.Ch. 5a

  DAave/min 4.1/3.8

Octupoles OFF => GF-reportParam 2b

(10seeds)

syst. err ON

rand. errors

ON (30%)

C.O.errors

OFF

DAave/min 3.03.2/2.73.0

+Sp.Ch. 5b“1002”

  2.9/2.5

1002 DAave=3.0 DAmin=2.9

1002 + SpCh DAave=2.9 DAmin=2.5

Octupoles OFF => GF-reportParam 2c

syst. err ON

rand. errors

ON (30%)

C.O.errors

ON

DAave/min2.83.0 /2.22.8“2067”:2.9/2.7

+Sp.Ch. 5c“2067”

  2.6/2.4

Octupoles OFF => Sp-Ch

Seed 2067: Ex=5.812e-5, Ey=4.969e-5, DAave=2.6 DAmin=2.4

W/O Sp-Ch 2.9/2.7

DA – Octupoles ON

Param 3a 2a

octup. ON OFF

syst. err OFF ON

rand. errors

OFF OFF

C.O.errors

OFF OFF

DAave/min +100: 3.3/3.0-100: 3.0/2.8

4.2/3.9 DA ave/min +50: 4.7/4.3

-50: 4.3/4.0

X-Y injection: -100 vs -50

X-Y injection: +100 vs +50

DA – Octupoles ON

Sp-Ch -> small effect (Octupoles too strong ?!)

X-Y injection: +100 vs +50 Param 3b 2a

octup. ON OFF

syst. err ON ON

rand. errors

OFF OFF

C.O.errors

OFF OFF

DA ave/min +100: 3.1/2.8-100: 2.9/2.6

4.2/3.9 DA ave/min +50: 3.5/3.2

-50: 3.5/3.3

+Sp.Ch. 6b 5a

DA ave/min +100: 3.1/2.9-100: 2.9/2.8 4.1/3.8

DA ave/min +50: 3.5/3.2-50: 3.5/3.2

X-Y injection: -100 vs -50

DA – Octupoles ON Param 3d 2c

octup. ON (100) OFF

syst. err ON ON

rand. errors

ON (30%) ON (30%)

C.O.errors

ON ON

DA ave/min+100: 2.22.5 / 1.92.2-100: 2.12.4 / 1.92.1

2.83.0 /2.22.8

DA ave/min seed “2067”:

+50: 2.6/2.4-50: 2.7/2.3

2.9/2.7

+Sp.Ch. 6d “2067” 5c“2067”

DA ave/min +100: 2.1/1.8-100: 2.0/1.6 2.6/2.4

DA ave/min +50: 2.4/1.8-50: 2.5/2.1

Present Status for beam loss

Lattices with 840 BBs for Sp-charge are prepared Laslett’s tunes = numerical tines with TWISS !!!Example: "BEAM2" for JF (nu_x=-0.090, nu_y=-0.145)N_particles=4.3e12; delta_nu_min=0.25; N_iter=5; TWISS-OK formula (-0.09054502765;-0.1435832589) => (18.749;18.586) twiss_sc_matrix_n.txt (18.750;18.586) twiss_bb_spch_0.txt (18.751;18.588)

twiss_bb_spch_makethin.txt (18.751;18.588)

GF-report: formula vs code• Beam1: -0.26 / -0.40 (-0.31 / -0.47) at 0.75x1011 particles per bunch• Beam2: - 0.18 / - 0.29 (-0.21 / -0.34) at 0.75x1011 particles per bunch

CPU-time for beam loss• my PC => 0.01sec/part/turn: 10 particles with 10^4 =>968sec 10^(-2)*10^3part*10^5turns=10^6sec =>

1.6*10^4min => 277hs => 12 daysCERN’s lxplus : 0.007sec/part/turn (30%):

Figure 10 Beam loss with space charge for Beam2 (2000 macroparticles) and 3x10^11 assumed total intensity.