HQ01 field quality study update

F. Borgnolutti, G. Chlachidze, J. DiMarco, H. Felice, P. Ferracin, M. Marchevsky, G.L. Sabbi, E. Todesco, X. Wang

HiLumi WP3 meeting on HQ test resultsAugust 2, 2012

2

Topics

28/2/2012

• Measurement accuracy (probe resolution)

• Coil block positioning tolerance

• Static behavior– Main field reproducibility– Geometric and iron saturation

• Dynamic behavior – Eddy current effect and Rc

– Multipole decay as a result of low Rc

3

Measurement accuracy

38/2/2012

0.0001

0.001

0.01

0.1

1

10

3 5 7 9 11 13 15

|bn|

, |an

| (u

nits

at

R.re

f = 2

1.55

mm

)

multipole order

normal

skew

Biot-Savart slope

peak

average

• Plateau of measured multipoles = probe resolution.

• 250 mm long probe: 0.006 units at 14 kA at probe radius (21.55 mm).

4

Resolution at Rref = 40 mm

48/2/2012

100 mm 250 mmn 880 A 14 kA s/n* 880 A 14 kA s/n*3 0.014 0.015 7.0 0.010 0.010 9.64 0.026 0.027 3.8 0.019 0.019 5.25 0.047 0.051 2.0 0.036 0.036 2.86 0.088 0.094 1.1 0.066 0.066 1.57 0.163 0.174 0.6 0.123 0.123 0.88 0.303 0.323 0.3 0.228 0.229 0.49 0.563 0.600 0.2 0.423 0.425 0.2

10 1.045 1.114 0.1 0.785 0.788 0.1

• FNAL working on a new probe.– A factor of ~12.5 increase in resolution for n = 6 with the same radius.

• Scaling from Rref = 21.55 mm to 40 mm.• Target resolution based on CM18 discussion: 0.1 units or better

System meets the minimum requirement up to n = 6

(*) s/n ratios calculated assuming 0.1 units harmonic amplitude.

Coil block positioning tolerance

8/2/2012 5

1.E-03

1.E-02

1.E-01

1.E+00

1 2 3 4 5 6 7 8 9 10

harm

onic

s σ

(uni

ts)

Harmonic order

fit

normal

skew

Rref = 21.55 mm

Best fit obtained with displacement σ=29.6 µm

• Harmonics measured at 12 kA using the 100 mm probe at 3 axial locations. Averaged from up- and down-ramps.

• Match measured σ with the one calculated for random block displacements. Uncertainty on σ is 50% with measurements at 3 locations. Will decrease to 25% with 9 locations (requires ~ 1 m long straight section).

• TQC/TQS coil block positioning σ: 36 µm – 64 µm. [Borgnolutti et al., IEEE TAS 19(3), p.1100, 2009]

• Comparable to the level of current LHC IR quads and main dipoles.

Main field reproducibility

8/2/2012 6

Normalized TF (two meas. shown)

• Two measurements from each probe. Each measurement = Precycle (to 10 kA) + 1 machine cycle (to 14 kA),

10 A/s.

• σ < 10 units below 6 kA (mainly related to “spikes” – much lower at 1.9K)• σ < 2.4 units up to 14 kA (may decrease with larger statistics)• Target: < 1 unit at 7 TeV. [E. Todesco, CM18 presentation, Indico]

σ (b2) of measurements from the same probe

0

2

4

6

8

10

12

0 2 4 6 8 10 12 14 16

Std

dev

of b

2 (u

nit)

Current (kA)

250 mm

100 mm

7

Geometric component and iron saturation

78/2/2012

• Geometric: 12.025 T/m/kA at 2 kA. • Iron saturation at 14 kA: -5.8% with respect to geometric value.

• Some discrepancy between measurement and calculation – Need to incorporate as-built coil geometry and changes due to cool-down and excitation.– Discrepancy changes slope at 10 kA – possibly more than one source.– Iron properties? Other?

11.2

11.3

11.4

11.5

11.6

11.7

11.8

11.9

12.0

12.1

12.2

0 2 4 6 8 10 12 14 16

Tran

sfer

func

tion

(T/

m/k

A)

Current (kA)

up

down

ave. meas.

Roxie

Opera

Rref = 40 mm-0.08

-0.06

-0.04

-0.02

0.00

0.02

0.04

0 2 4 6 8 10 12 14 16

ΔTF

(T/m

/kA

at

R.re

f = 4

0 m

m)

Current (kA)

meas. - calc.

8

Static b6

88/2/2012

• Shift the calculation with +4.5 units to match the measurement between 4 – 8 kA. – Calculation for nominal geometry at warm.

• Some discrepancy between measurement and calculation– Δ = -1.5 units at 14 kA corresponds to ~ 90 µm outward displacement of two mid-plane

blocks under Lorentz forces. – ANSYS shows ~ 30 µm.

-2

-1

0

1

2

3

4

5

6

0 2 4 6 8 10 12 14 16

b6 (u

nit

at R

.ref

= 4

0 m

m)

Current (kA)

Roxie, nominal

shifted

ave. meas.

-1.6

-1.4

-1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0 2 4 6 8 10 12 14 16

Δb6

(uni

t at

R.r

ef =

40

mm

)

Current (A)

meas - calc

9

Dynamic effect

98/2/2012

• Inter-strand eddy current dominates the dynamic effect.– Dynamic field error scales with ramp rate.– Decay time constant on the order of 10 s.

-10

0

10

20

30

40

50

60

70

0 10 20 30 40 50 60

Dyn

amic

sex

tupo

le [m

T]

Ramp rate [A/s]

B2

B3

B6

A3

A6

After subtracting static effectRaw data (static+dynamic component)

10

Calculation of Rc from sensitivity matrix

108/2/2012

• Solve a linear system: e = Sg. – e: field error vector; S: sensitivity matrix; g: conductance vector (g = 1/Rc).

B2 B6 B2 and B6

1=2=3=4 0.40 0.14 -

4=∞1= 2

-0.29

3 0.33

• Using field errors measured at 10 kA, 40 A/s.

• Assuming uniform Rc in block/layer to reduce the number of unknowns. Unique and physical solution not

always available.

Sensitivity factors computed from ROXIE

• Results suggest Rc ~ 0.1 – 0.4 μΩ.

Block Rc (µΩ)

Field error

11

Inverse calculation of Rc

118/2/2012

• Based on method originated from SSC and LHC. [Ogitsu et al., Particle Accelerators, 57, p. 215, 1997; Wolf et al., IEEE TAS 7(2), p. 797, 1997.]

• Error < 3.1% between measured and calculated field errors.• Rc lower in outer layer (0.2 – 0.22 µΩ).

• Goal: to match measured field error of B2 and B6.

12

Inverse calculation to match full error vector

128/2/2012

• Rc ~ 0.1 – 0.4 µΩ. – Error < 5% between calculated and measured dynamic field component.

– Consistent with 0.33 µΩ measured Rc on an HQ prototype cable. [Collings et al., IEEE TAS

21(3), p. 2367, 2011.]

• Top-bottom asymmetry in Rc (two different cables).

• Low Rc accompanied by high AC loss. To compare with loss measurement and quench behavior.

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0 20 40 60 80 100

Rc (μ

Ω)

Cable number

coil 5

7

8

9

5

8

7

9

13

Multipole decay at different current levels

138/2/2012

• Strong exponential decay in multipoles with τ ranges from 25 to 55 s.

• The decay of inter-strand eddy current due to low Rc.

-70

-60

-50

-40

-30

-20

-10

0

0 50 100 150 200 250 300

ΔTF

(uni

ts)

Time (s)

2 kA

4 kA

6 kA

8 kA

10 kA

12 kA

14 kA

• τ estimated ~ 40 s at 10 kA based on Rc of 0.3 µΩ in block 3 with quadrupole symmetry. [A. P. Verweij, Ph.D. thesis, 1995]

• Expectation with 20 µΩ Rc: τ reduces to the order of 0.1 s and negligible decay.

Rref = 40 mm

14

Conclusions

148/2/2012

• Current probe meets the minimum resolution requirement up to n = 6.• New probe being developed to improve accuracy at the same radius.• Plan to develop larger radius probes and anti-cryostats for future test.

• Coil block positioning error s ~ 30 μm at 12 kA, comparable to current IR quads and LHC main dipoles.

• Main field reproducibility at 14 kA (80% of SSL at 4.4 K) is < 2 units. May improve with larger statistics. Target is < 1 unit at 7 TeV.

• Harmonics as function of current are in general agreement with calculations. • Further analysis is in progress to understand differences up to 0.6% (TF) and 1.5 units

(b6).

• Rc between 0.1 – 0.4 μΩ obtained from direct and inverse calculations.• Consistent with 0.33 μΩ measured on an HQ01 prototype cable. • Responsible for large eddy current effect and multipole decay.• Cored cable was introduced in second generation coils.