AT-MAS/SCA. Verweij17 April 2007

Can CUDI be used for Can CUDI be used for decay and snap-back decay and snap-back

reduction and/or prediction?reduction and/or prediction?

Arjan Verweij, AT/MAS-SCArjan Verweij, AT/MAS-SC

AT-MAS/SCA. Verweij17 April 2007

Talk Nicholas:

Experimental data from SM18 give the best input of the expected decay in the different magnet types for a number of given current histories.

Scaling, which is required because tested magnets are not equal to the statistical mean in the machine, seems to work well.

Forecast to minimise decay not available.

Limited data available for different current histories

Possible solution: simulate the cause/origin of the decay, and then use these results to calculate the decay.

AT-MAS/SCA. Verweij17 April 2007 Origin of decay/snap-backOrigin of decay/snap-back

Decay is due to current re-distribution among the strands, causing field variations inside the cable, which in turn cause M variations because |dM/dB| is completely different for positive en negative B.

The origins of current redistribution are:- Redistribution of the transport current, due to non-uniform

joints/splices.- Boundary-Induced Coupling Currents (BICCs), induced

during ramping, mainly due to variations in dB/dt along the cable.

M

B

AT-MAS/SCA. Verweij17 April 2007 Origin of decay/snap-backOrigin of decay/snap-back

In a dipole magnet there are (per aperture):- 5 joints- about 2x4x15=120 strong d(dB/dt)/dz variations (inner layer)- about 2x4x25=200 strong d(dB/dt)/dz variations (outer layer)

Conclusion: The decay will be dominated by the BICCs.

Each boundary (or non-uniformity) in d(dB/dt)/dz will cause BICCs, diffusing through the cable. The local diffusion speed and amplitude increase depend on the local contact resistances.

Interference of the BICCs will occur because diffusion lengths are larger than half the magnet length.

AT-MAS/SCA. Verweij17 April 2007 Exact calculationExact calculation

Exact quantitative calculation of the BICCs and hence the decay is impossible in a magnet because:- the local Rc values are unknown- interference of the BICCs depends strongly on the cable transposition length

However, using CUDI –even on a relatively simple cable configuration- seems to give good qualitative correlation with the measured data.

AT-MAS/SCA. Verweij17 April 2007 CUDI (electrical module)CUDI (electrical module)

Picture courtesy of R. de Maria, CERN-AB

Typical discretization:1-4 mm3

tCM

tBA

tCMRCRCRC

ms

ms

ssccaa

1

Loop equations:

Nodal equations: 0sca CCC

Conservation of transport current: transportsa CCC

►

AT-MAS/SCA. Verweij17 April 2007 Input parameters Input parameters

Cable geometry: incl. return lead, mixed cables (s.c. strands + copper strands)

2 independently applied fields: arbitrary direction, variations along length and across width

Ra and Rc: variations along length and across width, local variations,

random distributions, soldered cables, zebra type cables, cables with non-uniform strand coating/oxidation, cores

Critical current: incl. variations per strand, local Ic variations (e.g. due to edge degradation, broken filaments etc)

SC-normal transition: ‘n-power’ or ‘matrix resistivity’ models

Strand resistivity: incl. local strand resistances (cold welds, broken strands, soldering to another cable)

Voltage taps: On single strands, or entire cable

Transport current: uniform or non-uniform distribution at the cable ends (simulating non-uniform cable joints)

Energy pulse: local or global (e.g. for stability and Minimum Quench Energy calculation)

Heat flow parameters: along the strand, to the adjacent and crossing strands, and to the helium

Currents: in strands, and in contacts Ra

and Rc

Powers: in strands, and in contacts Ra and Rc

Inter-filament coupling power

Resistivities of the strandsVoltages: resistive and inductive

Temperatures: of strands and surrounding helium

Self-fieldField along arbitrary line in

spaceMagnetisationHeat flows: in the strands, between the

strands, to the helium

Output parameters Output parameters

AT-MAS/SCA. Verweij17 April 2007 The ProgramThe Program

Input Data

Definition of the parameters (LabView)

CUDI.exe (executable FORTRAN code)

Excel or LabView based visualisation of the results

csv Data from other sources (field maps etc)

Output Data (csv format)

AT-MAS/SCA. Verweij17 April 2007 CUDI (electrical module)CUDI (electrical module)

1. Define a cable geometry2. Define a I(t) and B(t) cycle3. CUDI will then calculate, at user defined times:

1. the exact currents in all the elements of the circuit (i.e. Itransp + BICCs + ISCCs),

2. the field pattern next to the cable, or elsewhere (as a result of Itransp, BICCs, and ISCCs),

3. the magnetization M in each element of the circuit. Variation of M at constant Itransp is a measure for the decay.

AT-MAS/SCA. Verweij17 April 2007

z

dB/dt

Non-constant RA & RC, 4 (dB/dt)/dz boundaries

Constant RA & RC, 2 (dB/dt)/dz boundaries

z

dB/dt

low Rc low Rchigh Rcmedium Rc medium Rc

constant Rc

Model multiturn coil by a simple straight cable with a few RA, RC and dB/dt variations

AT-MAS/SCA. Verweij17 April 2007 Results for standard SM18 cycleResults for standard SM18 cycle

0

1500

3000

4500

6000

7500

9000

10500

12000

0 500 1000 1500 2000 2500

Time [s]

Cur

rent

[A]

-25

-20

-15

-10

-5

0

5

10

15

M [m

T]

CurrentMagn.

start precycle end injectionstart injection

AT-MAS/SCA. Verweij17 April 2007 Results for standard SM18 cycleResults for standard SM18 cycle

0.53

0.54

0.55

0.56

0.57

z-position along cable

Fiel

d ne

xt to

cab

le [T

]

at start precycleat start injectionat end (1000 s) injection

AT-MAS/SCA. Verweij17 April 2007 t_FTt_FT

-8

-7.5

-7

-6.5

-6

-5.5

-5

-4.5

-4

-3.5

-3

0 200 400 600 800 1000

Time at injection [s]

M [m

T]

60 s500 s1000 s1800 s

Decay vs flat-top time

0

0.5

1

1.5

2

2.5

3

3.5

0 500 1000 1500 2000 2500 3000 3500 4000TFT (s)

b3

(uni

ts)

AT-MAS/SCA. Verweij17 April 2007

-8

-7.5

-7

-6.5

-6

-5.5

-5

-4.5

-4

-3.5

-3

0 200 400 600 800 1000

Time at injection [s]

M [m

T]

4000 A6000 A8000 A10000 A11850 A

Decay vs flat-top current

I_FTI_FT

0

0.5

1

1.5

2

2.5

3

3.5

0 2000 4000 6000 8000 10000 12000 14000IFT (A)

b

3 (u

nits

)

AT-MAS/SCA. Verweij17 April 2007

-8

-7.5

-7

-6.5

-6

-5.5

-5

-4.5

-4

-3.5

-3

0 200 400 600 800 1000 1200

Time at injection [s]

M [m

T]

50 A/s30 A/s10 A/s

dI/dtdI/dt

-8

-7.5

-7

-6.5

-6

-5.5

-5

0 200 400 600 800 1000 1200

I (A)b 3

(uni

ts)

50A/s 30A/s 10A/s

AT-MAS/SCA. Verweij17 April 2007 Decay reduction by Decay reduction by

adding 400 s in 5 adding 400 s in 5 different waysdifferent ways

0

1000

2000

3000

4000

-300 0 300 600 900 1200 1500

0

1000

2000

3000

4000

-300 0 300 600 900 1200 1500

0

1000

2000

3000

4000

-300 0 300 600 900 1200 1500

0

1000

2000

3000

4000

-300 0 300 600 900 1200 1500

0

1000

2000

3000

4000

-300 0 300 600 900 1200 1500

AT-MAS/SCA. Verweij17 April 2007 Decay/snap-back reduction: Decay/snap-back reduction:

ResultsResults

-12

-10

-8

-6

-4

-2

0

-300 0 300 600 900 1200 1500

t-t_0 [s]

M [m

T]

+400 s at 760 A+400 s at 350 Avery slow increase from 350 A to 760 Aintermediate cycle to 2.3 kA+400 s at 760 A on precycle

AT-MAS/SCA. Verweij17 April 2007

You need time to get decay to 0 !!!!

AT-MAS/SCA. Verweij17 April 2007 Discussion/ConclusionDiscussion/Conclusion

CUDI calculates the cause of M decay/snap-back, i.e. the BICCs, and can therefore be used as a predictive model.

A very simple cable geometry gives already good qualitative agreement with data from SM18. Better quantitative agreement could be obtained by using a more sophisticated cable geometry. However, one should not expect to get perfect quantitative agreement.

Using CUDI seems a good way to select the best options for minimising the decay/snap-back in the machine, which then in turn can be experimentally validated in SM18.

It would be possible to run CUDI on-line with the machine, which would then give at any moment and for any current history approximative values of the BICCs, the field pattern along the magnet, the magnetization, and maximum possible decay/snap-back.