Bernhard Holzer

*

IP5

IP1IP2

IP8

IR 7

”Beam Dynamics for Nb3Sn dipoles ... latest news"

2

DS Upgrade Scenarios

M. Karppinen TE-MSC-ML

-4.5 m shifted in s

halo

+4.5 m shifted in s

transversely shifted by 4.5 cm

halo

Shift 12 Cryo-magnets, DFB, and connection cryostat in each DS

New ~3..3.5 m shorter Nb3Sn Dipoles (2 per DS)

May 2, 2011

Effects to be expected:

* magnets are shorter than MB Standards change of geometry distortion of design orbit

* R-Bends S-Bends edge focusing distortion of the optics tune shift, beta beat

* nonlinar transfer function (3.5 TeV) distortion of closed orbitto be corrected locally ??dedicated corrector coils ??trim power supply ??

* feed down effects from sagitta ?

* multipole effect on dynamic aperture ?

Sixtrack Tracking Simulations

Comparison: b3 Hysteresis Nb3Sn / NbTiM. Karppinen

The persistent current problem: Very First Multipole Estimates

b3 remanence as a function of precycle (pre-injection plateau) B. Auchmann

tracking studies & prototype measurements needed

Systematic errorsCurrent

(A) B1 b2 b3 b4 b5 b6 b7763 -0.7325 2.50 13.96 0.02 -0.24 0.00 0.29

1456 -1.3977 2.50 13.96 0.02 -0.24 0.00 0.292149 -2.0628 2.50 13.96 0.02 -0.24 0.00 0.292842 -2.7279 2.50 13.96 0.02 -0.24 0.00 0.293535 -3.3930 2.50 13.96 0.02 -0.24 0.00 0.294228 -4.0581 2.49 13.96 0.02 -0.24 0.00 0.294921 -4.7231 2.48 13.97 0.02 -0.24 0.00 0.295614 -5.3875 2.45 13.99 0.02 -0.23 0.00 0.296307 -6.0499 2.28 14.03 0.01 -0.23 0.00 0.297000 -6.7075 1.84 14.15 -0.01 -0.23 0.00 0.297692 -7.3565 1.05 14.31 -0.04 -0.21 0.00 0.298385 -7.9928 -0.21 14.36 -0.10 -0.18 0.00 0.299078 -8.6120 -2.13 14.21 -0.21 -0.17 -0.01 0.299771 -9.2204 -4.43 13.97 -0.31 -0.15 -0.01 0.29

10464 -9.8212 -6.94 13.68 -0.41 -0.14 -0.02 0.2911157 -10.4160 -9.68 13.37 -0.51 -0.13 -0.02 0.3011850 -11.0060 -12.49 13.06 -0.58 -0.13 -0.02 0.30

Nb3Sn Dipole: Multipole Errors, “Pure Estimation !!”

... in the usual units, i.e. 10 -4 referred to the usual ref radius = 17mm

Nb3Sn Dipole: Multipole Errors, “Pure Estimation !!”

NbTi Dipole: Multipole Errors:

Where are we ? IP1,2,5,IP7

Q8 Q9 Q10

Present Option: 2 x 5.5m Nb3Sn Dipoles separated

optics situationcollision optics, 7 TeV

no big difference in optical functions between injection / luminosity

b3 = 98, full & local correctionb3 = 98, no correction

ideal, linear machine

theory: phase space ellipse defined by optical parameters

Tracking Studies: Dynamic Aperture determined via stability / survival time

strong b3 multipole

Phase Space Distance

Tracking Studies: Dynamic Aperture determined via survival time

b3 = 98, no correction

survival time ... measured in number of turns ... gives an indication of the influence

of the non-linear fields on the ( an- ) harmonic oscillation of the particles.

x

yFor the experts: 60 seeds, 10^5 turns, 4-18 σ in units of 2, 30 particle pairs, 17 angles

Field Quality: Dynamic Aperture Studies7 TeV Case, luminosity optics (55cm)

ε=5*10-10 radm ( εn = 3.75μm)

ideal Nb3Sn dipolesmult. coeff. à la error table6

at high field the higher harmonics are small enough,the p.c. effects disappeared and the emittance is reduced (Liouville)

dynamic aperture for Nb3Sn

full error table (blue) b3 = 0an = bn = 0

Field Quality: Dynamic Aperture Studiesinjection optics, 450 GeV,influence of b3 values, 2 IP’s = 8 dipoles

dyn aperture injection optics, minimum of 60 seeds

the first estimated errors lead to

extreme reduction in dyn. aperture

main problem: b 3

dynamic aperture for Nb3Sn case: full error table (red) b3 reduced to 50% (green)b3 reduced to 25% (violett)b3 = 0 and to compare with: present LHC injection

for the experts: unlike to the collision case: at injection the b3 of the Nb3Sn dipoles is the driving force to the limit in dynamic aperture.A scan in b3 values has been performed and shows that values up to b3 ≈ 20 units are ok.

Field Quality: Dynamic Aperture StudiesInjection Optics, 450 GeV, Scan of b3

dyn aperture injection optics, minimum of 60 seeds

Field Quality: Dynamic Aperture StudiesInjection Optics, 450 GeV, Different Sectors

#2,7, an=bn=0

#1,2,5 b3=27#2,7 b3=27

#2,7 first estimate, “error table 2”

dyn aperture for Nb3Sn dipoles in #2,7 and in #1,2,5standard spool piece correctors

optimised for Q’ correction per octant

Field Quality: Dynamic Aperture StudiesInjection Optics, 450 GeV, ATS

#1,2,5 bn=20

#1,2,5 b3=0

#1,2,5 b3=27

#1,2,5 an=bn=0

dyn aperture for Nb3Sn dipoles #1,2,5ATS shows a increased sensitivity for higher multipoles, -> tighter limit for b3

and higher an / bn ATS Lattice

5.5 m 11 T Dipole Error Table Iinj Inom StdevB0 -0.758 -11.217  B/I -1.001 -0.947  Lmag 5300 5300 b2 -0.80 -14.41 1.93b3 41.33 5.20 1.24b4 0.09 -0.45 0.60b5 6.90 0.51 0.31b6 0.01 -0.02 0.18b7 -0.10 0.10 0.11b8 0.00 0.00 0.06b9 1.31 0.94 0.03b10 0.00 0.00 0.01b11 0.33 0.43 0.01b12 0.00 0.00  b13 0.00 0.00  a1 0.87 4.02 2.87a2 -0.02 -0.26 1.66a3 -0.11 -0.08 1.00a4 0.00 -0.01 0.64a5 0.09 0.09 0.38a6 0.00 0.00 0.20a7 0.03 0.03 0.09a8 0.00 0.00 0.05a9 0.00 0.00 0.03a10 0.00 0.00 0.02a11 0.00 0.00 0.01a12 0.00 0.00  a13 0.00 0.00  

Current Strength b1 b2 b3 b4 b5 b6

762.8948 0.746 104 -8.752 -23.648 2.856 6.020 -2.782

1.00E+03 0.983 104 -8.218 -37.815 -0.535 4.431 -4.096

a1 a2 a3 a4 a5 a6

0.0 14.981 -5.100 -6.927 1.632 7.834

0.0 48.483 0.924 0.392 2.680 11.107measured values for the “systematics”

FNAL

best guess for the ramndom errors

Mikko et al

Field Quality: Dynamic Aperture StudiesInjection Optics, 450 GeV, first measured values: “FNAL-demo-2”

ideal Nb3Sn dipoles,an=bn=0

first FNAL prototype systematics& Mikkos random artificially enhanced

b4...6 , a3

Field Quality: Dynamic Aperture StudiesInjection Optics, 450 GeV, first measured values: “FNAL-demo-2”

and again the tracking ...

systematics -> FNAL prototyperandom -> best guessuncertainty - > MB standard dipole

first measured values are just at the limit but at the moment in sufficient dynamic aperture is obtained.

Preliminary (!) Resumée:

first estimates / calculations for pc systematics ... where chilling

limits calculated for higher multipole coefficients (mainly b3)

first measurement results are “just within” these limits

problem: injection energy / opticslarge emittance, large p.c. effects

ATS injection / luminosity seems a bit more sensitive than LHC standard optics

unknown: realistic values for random errors ? do we have to deal with uncertainties ? limits for individual higher coefficients

Plan & Next Steps: follow up closely the new results

Particle Tracking Calculations

particle vector: field at particle position

x

x

)( 2221 zxg

xzgB

calculate kick on the particle

€

Δ x 1 =Bzlp /e

= 12

′ g p /e

l(x12 − z1

2) = 12

msextl(x12 − z1

2)

1111

1 //zlxml

epzxg

eplBz sext

x

Δ

Δ

xx

xxx

1

1

1

1

Δ

11

1

1

1

zzz

zz

and continue with the linear matrix transformations

Idea: calculate the particle coordiantes x, x´ through the linear lattice … using the matrix formalism. if you encounter a nonlinear element (e.g. sextupole): stop calculate explicitly the magnetic field at the particles coordinate