Main Ring+ Space charge effects

WHAT and HOW …

Alexander Molodozhentsevfor AP_MR Group

May 10, 2005

MR Injection process

Basic MR-design:

Injection time (Wkin=3 GeV) to accumulate the required beam intensityfrom RCS is about 0.17sec (in the case when just 5% of the total RCSbeam intensity is injected into MR).

The revolution period at the injection energy for MR is 5.38e-6 sec.

Then the injection process for MR is about 31’500 turns.

Feb.15,2005

Space charge tracking

General recommendation for the space-charge simulations

1. Transverse space-charge nodes should be at least 10 (or more) per one betatron oscillation

MR…Qx,y ~ 22, CRING = 1567.5 m, then LTSC ~ 7.5 m (~200 per ring nodes)

Our choice: TSC after each element and after LDRIFT < 3 m (~900 nodes per MR)

2. Number of macro-particles should be at least 10 per one mesh-point

…for the transverse mesh 32x32 minimum required number of the macro particles should be 10’000.

Our choice: time optimization … Nmp 10000

Feb.15,2005

ORBIT-MPI (TEAPOT tracker)

Single Processor.... DELL Latitude D600: Intel Pentium Centrino, 1.4GHzLinux RedHat 9

MR, 3GeV

1turn

MacroParticles

1'000mp 5'000mp 10'000mp 20'000mp 50'000mp 10'000mp+ BeamPipe

Pair-wise 23' 592.66'

Brute-Force PIC

22.22' 32x32

25.15'

FFT-PIC 32x32 40x40 32x32 32x32

~ 7’ 12.3' 30.9' 15.8'

1000 turns

1.9 h 3.4 h 8.6 h 4.4 h

10'000 turns

~ 19 h ~ 34 h ~ 86 h ~ 44 h

Estimation of time for simulation

Feb.15,2005

Longitudinal Nbin = 32

Comparison…

ORBIT-MPI

(J.Holmes,ORNL)

1 turn ~ 7’ (CPU)

ACCSIM4 *

(F.Jones,TRIUMF)

1turn ~ 30’ (CPU)

UAL

(N.Malitsky,BNL)

1 turn ~ 22’ (CPU)

* Including ACCSIM post-processing

Desktop PC-LINUXSingle processor

Notebook – LINUXSingle processor

Notebook – LINUXSingle processor

Feb.15,2005

Conditions: wp2, SpCh – ON … Nppb = 3.3e14/8, RF - ON, CCSX - OFF

2nd order MAD8 matrix Drift-Kick-Drift-Kick scheme:Q_split = 2 (kicks=8)BM_split =1 (kicks=4)

2nd order MAD8 matrixTeapot tracker:QM: (kicks=2)BM: (kicks=2)

Transverse space charge

• Pair-wise sum calculates the Coulomb force on one particle by summing the force

over all other particles. This method requires ~(np)2 operations to calculate the kicks, where np is the number of macro-particles.

• Brute-force PIC a straight forward PIC implementation. The macro particles are binned on

a prescribed X-Y grid, the force at each grid point is calculated using the

binned particle distribution, the force on each particle is calculated by a bi- linear interpolation from the grid. The operation time is ~(nbin)4.

• FFT-PIC … FFT method is used to calculate the force on the grid using the binned

particle distribution. The computation time is ~2nbin(nbin)2.

Feb.15,2005

Longitudinal space charge

• General way:

- bins the longitudinal beam profile;

- calculates the longitudinal space charge force;

- applies a momentum kick, based on the space charge force to the macro particles.

… the longitudinal profile of the beam is used as a weighting factor for

the transverse space charge kicks.

Couping the longitudinal motion into the transverse one:

… the space charge force on a given macro-particles is scaled according to the longitudinal charge density at its position in the bunch.

ORBIT-MPI test tracking

Wkin = 3GeV, Npb = 3.3e14/8 (h1=9)

RF-ON

ChromCorrection SX - ON

H1=9, VRF1 = 280kVH2=18, VRF2 = 140kV

‘Bare’ wp: Qx = 22.333 / Qy = 20.77

Gaussian Transverse:100% = 54 mm.mradRMS ~ 6.7 mm.mrad

Uniform Longitudinal:(p/p)MAX = 0.004()MAX = 60 degree

NSYNCH ~ 400 turns

ORBIT-MPI: Gaussian T-distribution Uniform L-distribution

Gaussian Transverse:100% = 54 RMS ~ 6.7

Qx=22.333Qy=20.774

Uniform Longitudinal:(p/p)MAX = 0.004()MAX = 60 degree

After 200 turns

2Q x-2Q y

=3

4Qy=83

-Qx+2Qy

=19

4Qx=

89

3Qx=

67

Qx+2Q

y=64

Qx + Q

y =43

2Qx-Q

y=2

4

3Qy=62

2Qx +Q

y =65

Gaussian TransverseDistribution

Kicks number(QM&BM) = 2 (in code=2)

SpCh – ON

CCSX - ON

ORBIT-MPI (Teapot tracker) test tracking

100% = 54 RMS ~ 6.8

Qx=22.333Qy=20.774

UAL test tracking

CCSX - ON

SpCh - ON

Gaussian TDUniform LD

Qx=22.333Qy=20.774

Kicks numberQM = 8 (in code=2)BM = 4 (in code=1)

100% = 54 RMS ~ 6.8

Steps … INJECTION & Acceleration

• COD

RANDOM BM-error (BL)/(BL)0 and H/V shift of QM so that to get some realistic COD (xCOD, yCOD) < 0.7 mm (TDR) … observation NORMAL SEXTUPOLE resonances & NORMAL OCTUPOLE resonances

• Misalignment

TILT of Sextupole Magnets … observation SKEW SEXTUPOLE resonances

TILT of Quadrupole Magnets … observation LINEAR COUPLING (skew) resonance

• Correction of Resonances …